> What would we exactly lose?

We'd lose composability and clearer code. This[1] section of the Haskell Wiki contains a good example.

In short, with something like this:

    any :: (a -> Bool) -> [a] -> Bool
    any f lst = or boolLst
      where boolLst = map f lst

the compiler can produce reasonably optimal code, because it doesn't have to convert the entire [a] to a [Bool], because of lazy evaluation -- when or encounters the first True, the map f lst expression stops being evaluated because of lazy evaluation.

[1] https://wiki.haskell.org/Non-strict_semantics#Why.3F