Why did Haskell, however, not try to fully evaluate addition,

like following?

(liftM . (+)) 1 [2] --->
liftM ((+) 1 [2]) --->
error

Haskell functions only consume one argument, not two. The composed function is applied to the first argument, which is 1. That returns a new function, which is applied to the next argument, which is [2].