Well, they could have thrown in Zatanna easily enough, though I think the characterization of Hawkgirl is hysterical (her idea of celebrating is to start a barfight, for example).
It’s not clear, though, if her wings are actually part of her or not.
On a semi-related note, in the episode in which Superman “dies” (“Hereafter”), J’onn sadly comments that Supes’ power had allowed the Leauge to win many battles “simply because he was there.” From my observation, though, Supes never turned the tide of battle by himself. He’d invariably end up in an endless slugfest with someone of comparable strength, or taken out by telepathy, magic, kryptonite, energy blasts, etc. Many of the episodes were written in such a way that Supes’s power gets neutralized almost immediately, leaving the actual victory to some clever ploy of (typically) Batman.
I can understand the problem, though. After all, if Supes went all-out, why would he even need the others?
It could be argued that this is exactly what Jonn meant. Without Superman there, it might take the whole league to stop just the one guy that Superman spends the whole time fighting. By occupying the most powerful member of the opposition, Superman frees the rest to deactivate bombs or whatever they need to do.