Why doesn't FullSimplify return -x working on Abs[x] and x<0?

Mathematica considers Times[-1,x] to be a more complex expression than Abs[x].

If you change the complexity function you can get the result you expect, e.g.

FullSimplify[Abs[x], x < 0, ComplexityFunction -> (Count[#, Abs, -1] &)]
(* -x *)