library is a situational card. unfortunately it doesn't have that many of its situations in base only, so it can make a bad impression. whereas smithy is pretty much always good as long as there is at least one player playing, because 3 is a good amount of cards to draw, library is only good when there are, quite roughly, 3ish cards that one would describe as Good With Library Cards. there are cards that look like they are those ones but are not: horse traders is an example. discard two cards, hey, that's what library likes, and i have another buy to get more Good With Library Cards! but in terms of actually, assuming that library is really your only good draw, then for this thing to work you need to, from the get go, draw two villages, horse traders, and library, and forget about whatever benefit you might get from playing the two cards you discarded (which is often not a concern but...). snore!
if you had a sour taste in your mouth after reading '2 villages' then you may be led to believe that most of the things that like library are non-terminal. the village ones that don't draw a card are fine but there aren't that many of them; warehouse and forager secretly library's best friends because they not only help out while increasing the amount of draw that library does, but also mitigate the biggest critical flaw library has which is that you need to draw quite well for it to work. also that library's other friends are expensive, which begs the question of whether they're true friends to begin with. library, like anal sex, is something that people seem to think you can just do without several stages of preparation.
however, when library talks she taaaaaaaalks; and when she walks she waaaaaaaaalks. if there's upwards of one village pile and all that jazz, it can draw 7 cards a lot of times, and there's even that weird other thing that it does that takes a lot of card text. vault/library is nothing less than an end goal of library, but it's really strong when that happens. but i urge you, reader, not to let god's light blind you. having ten pawns as well as library infrastructure and an other thing can double province consistently; two is a lot of provinces.