Nah, you guys are missing the beauty of rats. Rats are not really trashers -- every card that's trashed is replaced with a rat. But rats do temporarily turn all your trash cards into cantrips, at least until you start to run low on trash targets. But even if it's only for a couple of shuffles, having cantrips instead of dead cards could be exactly the help you need to get to your real trasher. And, as a bonus, when you do trash the rats, you get some cards, though you'll probably be drawing dead since most trashers are terminals.
The point is, you obviously need an actual trasher in conjunction with rats, but rats grease the wheels for you: they cycle your deck, putting that trasher in your hand more often. I think this will allow you to clear garbage from your deck much faster than normal.
It's not really a cantrip either, because when you play it, you have to trash something. So it decreases your hand size while not decreasing your deck size (though I guess it makes it move faster since the Rats cycle a little). This actually seems pretty horrible on its own. It seems like the point of Rats is to turn all your cheap cards into Rats so you get more out of your other TfB cards. It's just fuel generation. Bishoping a Copper gets +$1 +1 VP. Bishoping a Rats gets you +$1 +3 VP +1 Card. Copper remodels into at best a $2 card, but Rats goes up to $6, while drawing a card. It seems like the plan should be:
1. Buy Rats and TfB card
2. Turn everything into Rats
3. Trash the Rats for good stuff
It's not immediately obvious how fast this is, but since Rats are non-terminal, you can play a lot per turn once you get going, so it's probably good. I'm not sure Apprentice is the best combo, since you have to actually have something you want to draw, and it's going to be hard to buy that without money, since your Rats eat everything. Probably Upgrading or Remodeling cards are going to be the better combos.
Ok, someone out there is going to know this off the top of their head, probably:
How many TFB cards are there (anything that would make you consider buying Rats)?
vs
How many Discarding cards are there (anything that would make you consider buying Tunnel)?
Basically, what I want to know is, if we assume that Rats is only good for the TFB thing, will it be a completely dead Kingdom card more or less often than Tunnel? (Discounting the 2VP instead of 1VP for an Estate in the end-game).