I may or may not think of something more interesting to submit instead.
I had something else in the works but it was kind of convoluted so I scrapped it, haha.
That is so crazy good. It has got to cost more - $5, or maybe $6.
At $5, i'd give it a small nerf, like: "When gained, each other play gains a Silver".
This would be far too weak at $5, the price point of Sanctuary, a cantrip Exiler that is brilliant in all phases of the game.
Drachma on the other hand is a high skill card. You gotta manage timing and shuffling quite well for the card to do its job well. Keep in mind that, like with Secluded Shrine, having two copies of Drachma in play does not help you; they are both discarded when you gain the first Victory card.
Sanctuary, is proof that Drachma should cost at least $5. With Sanctuary it must collide with the card you want to Exile, which would require both luck and skill. Drachma is a low-skill card for it just sits there waiting - allowing it to be much more powerful/useful than Sanctuary.
Alternatively, making Drachma worth $1, instead of worth $2 would make this card's cost more reasonable at $4.
http://wiki.dominionstrategy.com/index.php/Exile
This is beyond wrong. Sanctuary does a plethora of useful things: Exile crap, gift you 3VPs that you would otherwise trash, provide an extra Buy, exile Green. And all without clogging your deck. It is a very centralizing card and you can run two or even three copies.
Drachma, well, would you open with it? Sure, if you would like that Silver to disappear, Drachma does that job (and unlike Sanctuary does not do anything anymore until you start to green). That is why there are likely better $4s or $3s to open with. In all other situations you only want it in the late game, shortly before you green. But you rarely want a Silver in this situation, a fairly crappy stop card. As already pointed out, Drachma does not work in two Provinces engines (well, it does, but you can only use one copy at a time).
So yeah, Sanctuary is overpowered and low skill whereas Drachma is tricky to evaluate, likely to be only good in some Kingdoms and thus a high skill card.