I understand the idea behind having Mew stay on Emerald, however, Mew is a Gen 1 Pokémon, it would made more sense to have him in those games.I agree with this. Especially since Emerald's event actually never made it outside of Japan. Even though it was fully translated the trigger never was released in any event outside of Japan. It technically never really appeared, in a situation not unlike the Azure Flute in the next generation.
Since nowadays legitimate ways of getting this Pokémon and also trade them in Gen 3 games is pretty much impossible, I would propose to, at the very least, make it possible to catch all 151 Gen 1 Pokémon.
There's ways to do this that still can make it feel authentic. In FR251 I put Mew in the Victory Road area where you fought Moltres in the original games. IIRC Pokemon Throwback actually put Moltres in it's original place, and put Mew on Mt. Ember where it could only be fought if you brought a Mewtwo with you. Either way, you'll have to modify one bit to make Mew obey (I forget where it was).