Frog was kissed by Marle, and he became a human again.
Maybe that really is the reason. In the PSX and DS ports, the ending cutscenes show a human Glenn being honoured by the King and Queen, regardless of whether or not you killed Magus.
One theory is that since Magus went back to 12,000 BC at the end of the game, he's considered dead as far as Glenn in 600 AD is concerned. Of course, there were similar situations in the game and his curse wasn't broken then, so the theory is flawed. Though perhaps it was because the entity Gates were still active or something (they're shut at the end of the game).
I beg to differ. Following your logic, Glenn should be human again at the end of the Moonlight Parade (after he goes back to his time), regardless of whether you killed Magus or not. But such is not the case. If you let Magus live, you can see Chrono & crew flying through 600 AD in the Epoch, and Glenn is standing there, on Zenan Bridge... As a frog.
If you did kill Magus, he'll be standing there as a human. I think we should just agree that the cutscenes, awesome as they may be, are full of sh*t. Because it also shows Glenn getting ("knighted?") by a bearded King Guardia, and if I recall, King Guardia in 600 AD didn't have a beard.
As for why the curse is only lifted if Magus is killed? I thought it made pretty much sense. Since Magus brought the spell upon him, it is lifted when he dies. And for the record, I don't recall Magus saying the curse will be lifted if you kill him on North Cape. He just says "...You wish to fight me?".