Is there any real reason why we can't trade Potions?
Like I can't think of a good reason why we shouldn't.

Only reasons I can come up with are:
(1) So the Broker isn't flooded with potions - I have 1,436 of one potion, 1,620 of another potion, 1,802 of another potion and 1,621 of a final potion in my Inventory (and those are only the ones I might use).
(2) To prevent people from being able to access potions that are too advanced for their level (e.g. a level 10 user having access to a potion which could be used to heal a pet back to 100% health even if its down to like 0 - 1%).

Ultimately, I'm not aware of any specific reason but its never particular affected my gaming experience.

That makes sense.

The reason I wanted to know was because I wanted to send a few that I'm not going to use to a user who's stuck on one of the bosses. The ones you can buy are generally not the best I've found.

Yep, unfortunately you can't send them to another user.

Best way to get good potions is definitely Missions (the higher the better) so definitely suggest to the user who's burning through potions to make sure they're doing Missions as often as possible :)

Edit: Just went to check and you can get the 2,400 health healers in Ethernia's Armory (1,600 healers in Saerielle's Armory) so its possible to pick up decent potions in the towns but I have a general impression that you're generally one potion level behind what would be really really helpful when you're working through a particular area.