I think the general thinking/concern here is that the roots can choke themselves off (and kill the tree) through growing in these non-standard shapes- the main concern would be if the tree is going to choke itself off before it produces much (or any) fruit. If you really love trees like this I would suggest doing spaced out plantings in pots (every 3-5 years) to ensure you do not have to be without a producing tree for the full juvenile period of a new tree. (They WILL die eventually, but could be like 30 years)
There is some debate (at least with Mangoes) if root structure impacts fruit quality- I don't think there is a consensus in mangoes, and if not there then certainly not in other species