>>2365676To be specific, let's take another look at OP's picture of the trees he has inherited from the previous owner. Let me first say that I do love box elders, they are weedy and can be very invasive but are attractive when they have room to grow and are the main host to one of my all time favorite mushrooms
>>2358179 Now this is all stuff you should know already, being a genius self-taught dendrologist but let's go over it anyways. One of the main issues with box elder pertaining to OP's yard is they are prone to disease and have very weak wood. They grow well in boggy soil but because of root rot are very unstable. Go mushroom hunting for elm oysters and you'll see many of the trees are cracked and blown over.
This is probably why the previous owner tried to kill it by cutting it at the ground. He was an idiot in not removing it outright because now he just coppiced it for no reason. If left unattended those shoots will all get bigger and heavier and start cracking off in storms opening up the tree to even more disease. Best case scenario this tree limps along for another decade or so while it rots at the core and it's limbs die.
As for why the previous owner wanted it removed in the first place again is related and why they are mostly known as weed trees and rarely planted purposefully. When let to grow properly in urban settings they're an even bigger liability. Seeing as this is literally growing through a fence it probably wasn't planted purposefully in the first place. Let to grow large in swampy soil like this is just a matter of time before a large limb snaps in a storm and causes property damage to himself or someone else he'll have to pay it to.
OP asked a very good question, which is what is something better suited to actuly thrive there. You seem to be saying he should not remove these trees and you have deep knowledge in this area, so if that's your reasoning then explain why you think so.
