I notice now you actually said 'cards', not actions. So I suppose Platinum qualifies as it gives $5, and is a treasure so "non-terminal". Similarly I guess Bank can sometimes qualify, and Lio rightfully points out Death Cart can also give $5, and it's trashing is sometimes a benefit, so I guess that kinda counts as well. Beyond that... I can't think of much. Adventurer can give at least $4. Pirate Ship can give arbitrary amounts, but it's slow to do that and gives no other benefits. Vault, Secret Chamber and Storeroom can give more money than that, with other benefits - but that $4 comes at a huge cost of a big chunk of hand size.
Precisely. When I consider a card's "usefulness" I consider it with respect to its individual cost, what its synergies are, and also its opportunity cost (buying that card, as opposed to another card of equal cost) among other things. I know transmute is a bad card generally, but all it costs is a measly potion to get it. Also, there are certain boards where I feel like it can shine, (ie: if it's the only trasher card or other alchemy-based synergies are present). I think on boards that are predominantly alchemy-based, it's a decent choice because you can use it to get an early gold on a 4/3 split by simply buying a potion.
Now don't get me wrong. I don't think Harvest is the best $5 ever, or even really an especially good one. But if there were a $5 card which just said "+$4", I think it'd be up there with the power $5's. That's a lot of economy from just one action. Of course that isn't what Harvest does. The way it works means earlygame, +$2 is quite likely, while later on +$3 is common and +$4 happens more than +$2, but if you draw your whole deck, then there's a good chance Harvest is just dead. That makes it... pretty tough to make work to a level which is worth the buy, but it can be done, it's not unreasonable. For that reason, I think it's a weaker $5 card, but not the worst $5, and certainly not the worst card.
If there was a $5 card which just said "$+4", not only would it be up there with the power 5's, it'd just be completely over-powered. But indeed there are cards that can give you +$4 much more easily. The example that comes to my mind is Poor House, which at a cost of $1, is the cheapest card in the entire game. And as you pointed out, the effect of Harvest is way different than merely giving you $4. In fact, the chances of getting that $4 using Harvest is very, very slim because in order to take advantage of it, you'd literally have to base your deck around Harvest (and being that it's a terminal action, that's not a very good idea). The only other time I could see it as potentially useful is if your deck was filled up with junk (like curses, coppers, estates, ruins, or other garbage) and there was simply no other options to discard for benefit and gain more cards. But if your deck is already that bloated with junk, you're probably going to lose the game anyway.
Maybe it's not the overall worst card in Dominion... especially with stinkers like Duchess, Scout and Thief, but in terms of value, I think it is the worst in the game. At least Duchess, Scout, and Thief are reasonably priced ($2/$4) and have situational-type benefits. Same thing applies to Transmute, Secret Chamber, Moat, and so on. I just don't see a situational benefit to Harvest because there's almost always a <=$5 card that would be more useful given any particular subset of cards. Just my two cents though.