Most woody entities make deep roots. Any that do should love this, like a Dracaena, Schefflera, false Aralia, Gardenia. Probably mandarin as well but not something I'm qualified to suggest.
A pot that shape will be more likely to tip-over if outside when windy.
But if it does not have a hole in the bottom for excess water to drain out, it might be best used as a cache pot. If it is difficult to find a pot that fits in without falling in too far, you can put some rocks or bricks in there until the inner pot rests at the desired level.
