I hadn't even thought of curse-trashing as a part of this discussion, but it feels so good when my opponent buys a couple of Familiars and I'm able to keep up defensively, even with just weak trashing available; I'm able to improve my deck while my opponent spends most of his resources attacking me. I recall a Familiar game with only Lookout and Watchtower for defense, but I was easily able to keep up with the curses because I was able to get my watchtowers in hand more often from lookout-trashing.
Curse trashing is a pretty big reason to go into trashing. Now I won't take transmute (no other potion card) just to deal with the curses, but going something like trade route, salvager, or some other generally weak trashing can be worth it on some curse boards. If my opponent goes strong trashing, on some boards that is enough to shift my strategy away from cursing and towards another (like engine building). Familiar is one of the strongest examples of a curse giver that can be deterred by strong trashing - you rarely want familiar against a chapel deck.
I'm all about this, but the thing I thought of before I got to your list were attack cards, mainly Ghost Ship. I've made some awesome comebacks with a CR-draw engine after six provinces were gone by playing a ghost ship every turn. I've also been on the receiving end of an engine with a single University that picks up Labs, then Militia-Masquerade as the kicker. I needed just one more Province to ice the game, but I was never going to buy a Province again after getting hit with that every turn. You addressed attacks separately, so I guess you mean something different by this that I must be missing...
Sure, let's say your opponent goes for Nv/Bridge. You go for possession. Your goal is to be able to play possession every turn. Trashing down to a small hand, buying silver-silver-gold-pot-possession means that you can steal the megaturn whenever is most advantageous. Your deck revolves around playing one card; play it and you win. Likewise, let's say you have Plat/adventurer (a weak combo, but hey), you have one card (adventurer) that you want to see over and over again. Trashing hard to get down to where you will see that card most every hand works well.
Or let's take a HoP deck. When building a strong HoP deck, you want trash out duplicate cards, load up on cheap-no terminals and maybe have one each non-HoP treasure. When your HoP gets up to 5 coin, you cascade HoPs (HoPs gain other HoPs) and then you have your one megaturn when the HoPs get worth 8 and cash out. For this type of deck, the key is to play HoP over and over again. Sure you might be using it to gain crap like pawn, pearl diver, village, and walled village ... but the key is one card does it all for you - HoP gains you your enablers (cheap non-terminals), HoP gains you your payload (more HoPs), and HoP gains you your payout (provinces). Heavy trashing is extremely useful when rather than buying more economy (e.g. plats), you can just use the ones you have more often.
Strong Trashing vs. Weak Trashing... I'll admit I've never thought to take the weak option over the strong option before because it would actually be better, but then again, I'm not a level-40 player, and that seems like a level-40 concept...
This is silly, but the way I think about this is a graph (I'm a math guy). The X-axis is turns, and the Y-axis has a few things super-imposed on it. First is number of bad cards left in my deck (I think of this as "deck potency" or "deck awesomeness"). Second is total buying power of my deck (Have to make sure this doesn't go below $3, and if it hits exactly $3, your deck better not be Mint-CCEEE-(Pawn/Copper/Herbalist), because good luck drawing all three of your dollars in a given turn -- I learned that one the hard way). Third is the number of good cards in your deck. The danger here is to let your deck potency get too high too quick (what dondon was talking about). But if you don't see your Chapel until turn 5, you don't want to let your deck potency get too low too quick either, or else you won't see your trasher often enough and you won't be able to line it up with the cards you want to trash as easily. Balancing these curves on the graph is super-tricky, and how you do it depends heavily on shuffle luck. The strategy for Ambassador has been talked about a lot, but other strong trashers haven't been given the same treatment. Is there any kingdom-invariant advice that anybody can provide here?
In a word, No.
Sometimes chapel will be amazing. Chapel/squire/goons/village is a gimme chapel/squire opening almost. Other times, like Fg/Chap, the trashing hurts you too much early to be worth it. As Dondon notes, at some point trashing coppers is counterproductive, but that varies heavily by deck type. It doesn't take much for something like Border Village/Margrave to want keep some coppers around (this combo is strong enough that I might even just forgo chapel) and prefer TfBs like remake or remodel to chapel. On the other hand some combos, like pin decks, discard/masq, or Kc/Mountebank are so strong that you want to get rid of your coppers the moment you no longer need them to buy your components.
I mean some things just get really crazy here. Smugglers means that you can ignore your economy and just mooch off the other guy ... unless he goes for Kc engine and stops buying non-Kc components before you get setup as well.
My take-away from that was that the objective was to play the Goons card as many times as possible. Anything that helped play more Goons was helpful, which included trashing. Maybe I just mis-interpreted this? Perhaps it's better to almost play a BM-variant where your goal is $6 instead of $8, and only add trashing if there is little-to-no opportunity cost associated with it?
It depends. Like I noted steward is great for goons games - you can either trash crud out of a hand that won't buy a goons or you can buy the goons. Likewise, cards like squire, smugglers, remodel, etc. can all let you bootstrap into goons for a decent tradeoff; however you do have to be aware - Goons is harsh because:
1. It interferes heavily with trashing - often forcing you to choose between trashing two cards or buying a silver.
2. The only way to buy a goons after you've been hit with one is to have 3 silvers (or equivalent) in hand. This makes goons a race card. Winning the race results in decent odds of a compounding advantage - by the time they can buy their first goons, you have bought 3 and they can never play as many goons.
3. Playing sooner gives them more VP chips. Yeah it isn't a lot, but any lead in a goons game can be strong - either to give you a chance to go green and end the game before they can cash out for mega chips or force them closer to 3 piles if they build their own engine.
OK I know I mentioned this above, but I guess I have one thing to add related to cursing attacks. Sometimes I'll see an engine board with a curser on it and strong trashing. Both me and my opponent ignore the curser at the start and build our engines. But once or twice I've pulled this move: at the point where I can draw my whole deck (or at least most of it), I'll use my buys to pick up one or two copies of the curser, and on the very next turn, before my opponent can really react, I will pump a ton of Curses into their deck super-quickly (KC helps a lot here). Getting the initiative on this is like pouring a bucket of water on their nice engine, and the 1-turn tempo loss I get from this is totally worth the 4 or 5 turns my opponent loses by having to clean up the mess I made in their deck. This seems powerful if you can do it quickly enough that your opponent doesn't have time to react, and they can't clean it up all that fast. Is there a good counter for this, other than getting to it first?
Sure - the turn after you buy the curse givers I buy some TfB's and additional draw. You give me say 4 curses, I play my engine and then trash all 4 curses. Chapel in a strong engine deck (one that draw the whole deck) laughs this stuff off easily, forge is also great at counter this. I can also play around with reactions (trader, moat, watchtower) - particularly if I have any top deck control, reflections (ambassador or masq), and racing - if we've depleted two piles building our engines you may have just dumped half the curses on me ... but they go into my discard so I might be able to buy two provinces and the rest of the curses for a 2 point win (or a colony, an estate, and the rest of the curses; or if I have a strong reaction like Wt or trader somewhere in my deck).
At the end of it, you normally give up at LEAST a province for this. Take the Kc case if there are ANY +2 actions you could get instead of the curse givers, you'd have made 12 coin instead the next turn and netted 6 VP (the same differential you got from cursing me). If my engine is strong enough to deal with the curses, then I just Kc my trashing and deal with them.
Your strat works really well against trashing that can only hit coppers and against trashing that is gone from the deck (island on the chapel, Procession or Grave robber being used on the trashing card, etc.). It works less well when the opponent doesn't have & can't buy the draw to deal with six curses. It works better when you can hit closer to a shuffle - but strong Kc engines rarely leave more than 5 cards in the draw deck. It works extremely well if the other guy has not built a very robust engine or no engine at all.