They will re-sprout, in fact the trunk can be ground down below ground level and a few years later it does its Phoenix
thing and rises from the ashes.
But, what rises may be a clump that spreads too wide for the space.

If you take them out you'll need to dig out a huge amount of core root area. If you leave some, it could return.
Do you plant to replant something else in place of the crapes? If so, you'll want to be certain to get all the core roots and most of the side roots.

I had an 8 year old Natchez that was blocking a view. Armed with a mattock hoe, shovel, large pruners and a chain saw I went to dig it up. Ha! I cut 13 lateral roots and then hit it with a sledge hammer and it did not budge. A man must know his limitations. Cut it off slightly below ground level. The next year it sprouted and grew to about 8 feet tall and bloomed in August!

I cut back, round up on it etc. Spouts coming up each year. I finally hired a guy with a ditch digger that came and dug it up in about 40 minutes. This was an area that was fairly moist.

Cut them down to 12 inches and spray stumps with Brush Killer, wait a month for new growth to emerge, spray that with Brush Killer, repeat 12 times. They might die then, with luck.

Buy something new for the other area.

You could always move to another home..I did that to get away from Bermuda grass.

(I wasn't kidding!)
Don't wonder why the towns and cities plant these things in the medians of 4 lane roads.
No matter how many times these crapes get run over by cars/trucks they come back up.