Actually, if you think about it, this is better because summon capsules are restricted by racial alignment.
Oh, but the glitch to leave the partner mount sitting around without being used is fun too. There also seems to be a way to force your partner to have rest active while up and running around. Although, I haven't bothered to confirm if the recovery effects continue to apply.
So, if you just dismounted from their broom, and your press the mount pet hotkey, you will proceed to mount the broom again. I haven't actively tested to see if this carries between summons, though.