Yoshida-san has been all about compromise with everythign else. I don't see why they couldn't make the pet optional. If you have it your strength is split between wyvern and dragoon. Also make it so the wyvern only gets K.O.'d when you do and not by itself, so you can't suddenly be knocked down to half strength.
It could be quested, and those who choose not to use it remain at full strength.
There could be lore that makes sense for those who choose to have a wyvern companion.

I don't think I'll play dragoon without a wyvern personally. It just doesn't fit my character.