I would like it.
Other platforms (PSP, PSVita, PS2, ... (not Sony fan at all xD)) have almost always at least 3 save slots so why can't Pokemon?
Trading and Mystery Gifts could be done with a bit of programming, I believe...
The share of one game can from one point of view be disadvantageous for the GF in terms of money but on the other hand, groups could buy one copy together and play it on different saves.
But the main reason is the one I mentioned in the second sentence. If others can have it, why Pokemon can't?