It's normal growth on a tree or bush when man doesn't work to keep it conforming to some predetermined shape or size.

But having said that, I would trim them because of wanting to keep the overall round shape.

I would probably trim the bottommost left and right branches also, because they are reaching up for the light and have long lengths without any leaves to benefit the tree.

Alternatively, they are also good choices for air layering so that you can get 2 new trees from them, if you feel inclined to do that.

You probably mean purple leaved plum not pear.

Pruning is just man trying to make it look like he wants it to look.

You are correct! Plum This was a bare root from the Arbor Day foundation.