Stashing Pets

So I accidentally bought a plat pet on my warrior, asked support if they could transfer it to my mage character, which they said no to.
I realize that's probably just a waste of time for them.
So I don't see why we should be unable to stash them. I guess it is so you couldn't powerlevel your new character with a 36 pet or use a 36 pet in level 10 pvp.
So why not make pets below level 5 stashable, or level 1 pets only. Along with that an option to reset your pet to level one would be nice.
Any ideas or problems?
Devs?

This defeats the purpose of buying pets on another account. The egg economy will reach a downturn and sales will fall. Cuz its like a "ooooh i have malison on this guy, im gonna transfer it to this guy so he can use it too!" kinda thing. Buying pets would be like buying more than one lepre.

This would be abused. You could just transfer all the pets around to your different characters in order to get beastmaster and other pet APs.

BTW, you should have just told support that you pressed the purchase button by accident and ask them to take back the pet and give you a refund. If it was your first time asking for this sort of thing, they would grant it to you. They just don't want to be bothered doing these favors for the same players over and over. But they are reasonable and do appreciate that you buy plat.

I think this would have been a more reasonable request than to transfer a pet, which as I mentioned, can be abused.

Yeh I see what you are saying, but I feel like it limits the amount you try other classes when you have to drop another several hundred plat or a few mil on a decent pet. Odds are you will just stick with your stacked character.
Obviously it would lower demand slightly, but if you wanted a capped pet on all yours chars you still would need to buy multiple.