I’d throw Irving Berlin on that list, and possibly Mercer’s occasional partner Hoagy Carmichael.
Mercer is often overlooked because he arrives somewhat later than the big three, i.e. after Tin Pan Alley had had it’s heyday. But he’s at least their equal musically.
Understood. So think of it as choosing your five favorite masterpieces. Selecting the ones you like the most, without implying that the others are inferior.