Not only are these strategies not dominant, they're not even good. I'm not comparing embargo/gardens to ironworks/gardens - there's no comparison. One is the strongest 2 card combo in the game, the other is worse than BM on almost every board. The point is that the embargo slows you down a LOT, exactly because you trash it, and of course the curses slow you down too if you're embargoing gardens. And without good enablers, gardens is too slow/weak anyway. With most enablers, you should be doing other things with your important time. Also, basically every enabler does care about you having junk in your deck, as you want to play those enablers often.
Okay, let's break down your specific strategies. Ironworks/islands I'm fairly sure would lose to ironworks/gardens, but at any rate it's totally irrelevant, because on any board you could choose between those strategies, you should be going for ironworks/island/gardens. Goons/Gardens will be far too slow to do anything against ironworks/gardens, even if you do get the goons on turn 3. Vineyards/ironworks is even slower - you'll never get nearly enough vineyards before the game is over.
Your strategy from edit2: by the time you empty the embargo pile and the gardens pile, the game is probably over and you've lost.
First strategy from edit3: I'm not sure, but they may still be able to just go big money and win. You'll be extremely slow to get the gardens, and they won't be that strong when you do. What I am sure of is that they can just cut you off from gardens by buying 5+ themselves and/or getting at least a significant number of them and scarfing up duchies, which they'll be much better at doing than you, 'cause you've wasted all this time with embargo.
Finally baron/gardens/embargo. In fact it does take quite a long time to get all the gardens, estates, curses, and 6ish barons. Long enough that the opponent would have all the provinces just playing BMX before you get there. They could even wait quite a long time and still win.
And certainly not every gardens strategy needs to be a rush, but games of dominion are fast generally, so usually you need to be fast to win. But something like bureaucrat with gardens and being able to grab a couple provinces too is quite strong. But these are all more mixed strategies than straight-up gardens decks.
My point about ironworks/garden was that people kept throwing that into the discussion as if it were vaguely relevant (basically the i/g discussion stemmed from an anecdote of the original poster and somehow dominated some people's posts). It's clear that if these two cards are present, the embargo essentially is useless besides annoying big money. Now you seem to argue that even that is not true. I can assure you that if you open 5/2, you will want to buy ironworks/embargo, not ironworks/estate or Ironworks/copper if you know you are going against BM. And I'm pretty sure you'll want to embargo gold or gardens in that case. It may sound trivial, but is actually relevant to the topic.
Now the initial discussion was about the interactions between gardens and embargo: trying to figure out when they could potentially interact. As I argued (and you agreed on this part, though you make it sound like it's your idea, when all you said was "omg, gardens/ironworks pawns"), is that in the presence of gainers, you will not go for embargo, except
maybe to annoy BM.
The point I was making is that, in the presence of low quality enablers, typically market/embargo or worker village/embargo, you can double buy/double play embargoes very early, on, severely embargoing the provinces before a standard BM strategy has had the chance to get one. Start embargoing gold. To get it's first province, BM usually needs 2 gold. That means two curses. That'll slow it down a bit. I'm pretty sure you should be able to distribute a curse on gold and 3 curses on provinces before BM gets it's first province. If that doesn't handicap your BM strategy, then I want your shuffling skills please. The point being that any tempo loss you have at the beginning will easily be compensated by the fact that you are slowing down the game a lot, and have the right deck shape to win a gardens race if he decides to switch. If he doesn't, you could win anyway. Again, needs to be tested, but trying to impose your "ironworks/gardens" metric on a game that plays completely different might be off. You might be right, but for the wrong reasons.
Now the the specific points:
- I insist. If you already have the points to win and just need to finish, whether the junk in your deck is curses or estates does not matter to you. Curses empty a lot faster than estates when something is embargoed. And horse trader doesn't care if the k crap cards in your deck are estates or curses. Now the question is whether finishing 3-4 turns earlier is worth the (quite significant) point difference. That depends on a lot of things. Saying curses are more trash than estate for the functioning of your (non baron) deck shows a serious lack of understanding of dominion mechanics. Sure, you want to hit your enablers more often. But you want to empty 3 piles. Assuming you finish on gardens, that means you will actually only have to empty 2 piles: whatever your first pile is, and the gardens/curse pile. So we essentially want to compare emptying 1 pile + estate + garden or 1 pile + garden/curses. Regardless of how you put it, if you don't care about the points given by estate (assume the other guy is building some kind of engine), the second scenario will end before the first (with enablers that don't gain nor interact with estates). Now whether that wins or not depends on the board. It probably doesn't but for a completely different reason than the one you gave: not because you hit your enablers less often.
-I think the island is the
critical decision in a garden/ironworks/island pool. You have clearly not put an awful lot of thought into that one, just assuming that it, again, fits one of your preconceived schemes. Obviously both players will rush the ironworks pile, trying to get an edge on those. Assuming a 5-5 split, however, the next important strategic decision is whether to get more islands or more gardens. I am unsure what the answer is, though I would suspect the player that biases his selection a bit more towards islands might have an edge. Again, needs to be tested, but declaring this decision to be trivial seems like you rely on preconceptions a lot. They might happen to be true, but you certainly have not proved/thought about it.
-Goons/gardens with goons T3 means
at least 6vp from goons. It takes 3 full deck cycles for ironworks T3 onwards to empty gardens. Goons can splash an iron work, or just steal gardens early on and should get a 3-5 split (at least every time he plays a goon he can grab a garden, so 3 cycles means 3 gardens). Depending on what else is on the board, he might very well win.
-ironworks/vineyard means a 5-5 split in terms of ironworks. If there is a good 3- action (ware house/cellar/pawn/hamlet) vineyards could play both on the gardens and vineyard front, but the vineyards will yield more points than estates. He might get a 3-5 or even 2-6 split on gardens, but the vineyards might overcome that deficit. The thing is, all these strategies can steal gardens from the gardener, because they fit their strategy too.
-Refer to the market/embargo opening. You don't need to empty the embargo pile to cripple BM. if you embargo gold on T3 and provinces from T5-T7 on, BM is not going to finish any time soon.
-Barons/embargo/gardens sounds too slow indeed if they get their early gold, as I assumed.
Gardens strategies tend to rush because if you give away 2 or 3 extra turns, oops, your opponent playing straight Big Money outscored you on Provinces alone.
I have yet to win a game with BM, and my ranking is OK. I would even go as far as saying that I win more games playing bridge-combo (usually against BMX) than with BM. Not that I disregard the strategy. It's a good baseline. But please, don't stifle creativity just because bots can't handle it. Sometimes you need to go a bit further than just \epsilon away from the equilibrium to find a new, potentially better one. Often you fail. But if you never try because of preconceptions, then you become a bot.