Okay, that's an improvement. Now about the cost. I don't see whole $1 gap thing as an issue. In this case, since it's a cantrip, it usually improves Upgrade/Remake since Rats will usually be better than nothing.
What you're saying will be true in some cases. But with some handsize-increasing and/or trashing, it will often be relatively easy to be playing multiple Rats quite regularly. Also, there are plenty of other cards that often "don't do anything". Menagerie, Village, Pearl Diver, Hamlet, Shanty Town, just off the top of my head. I suppose it's most directly comparable with Fool's Gold. It doesn't really matter that the first one does nothing, because if you're playing with a plan, you're not going to buy exactly one.
As I've said before, if you can get them going, they're worth somewhere between a Village and a Lab (probably less though, as you'll often play an odd amount). I would say they're better than the likes of Pearl Diver, because there will be times when you REALLY want even the minimal extra actions you can get from Rats.
So I would probably price them around the $3 or $4 range. But hey, if you particularly want them to be $1, I don't think it would be game-breaking, just a little underpriced. And of course if you think that's the price that would bring the most enjoyment to the game, then that's the best reason for any sort of decision like this.