On the other hand, when someone reads "echo LOOK_AHEAD" they immediately know it's a constant and thus (a) global and (b)(more importantly) defined once and never modified by the code.

With "echo $look_ahead" there's no indication of that, and in the future another dev might add something that modifies $look_ahead's value and break other parts of the code, making for sneaky bug (which incidentally is why non-constant globals are so disliked ;))