You're stopping the Rat population from overwhelming your deck, though I suppose Watchtower trashes what you don't want and Trader is a trash for benefit of a sorts (not only the reaction but the regular action makes it a trash for benefit). Hinterlands and Dark Ages are sort of a ying-yang that was (particularly Feodum thrives on silver which many Hinterlands cards make it easier to get; Trader, Border Village, Embassy, Haggler, Noble Brigand, Jack of All Trades). There is probably a good combo with Rat / Trader / Feodum allowing you to breed Rats to change into silver to buy Feodums which get more powerful with the more silver you have.
Rats also feeds on enemy cursing attacks (making them less powerful though possibly giving you a Rat problem).
I would actually be interested in the secret history of Rat. $4 seems to be the right price point as it would be less useful at $3 and more powerful at $5 (particularly with trash for benefit on the board).
It's not even that simple. On the copper front, Cache gives you some, Ill Gotten Gains can get you some, and Goons engines often result in using the extra buys to get copper. The copper becomes Rat food. Trader can turn the Rat you would have gotten into silver and Watchtower can trash the Rat (both giving you the kicker for trashing a Rat).
Of course, it might be simpler just to use Trader/Watchtower on those coppers, so I'm not sure Rats is really adding anything here.
I think all the comments so far have assumed - as we usually do - a two-player game. But with three or four players the rat pile could empty quite quickly, and once the rat pile is empty Rats becomes merely a non-terminal trasher. The interesting part will be the strategy about who buys a Rats first, because if only one player does then he likely won't be able to play Rats (without some other trashing card available) without the rats consuming his whole deck.