You probably could, but why not just cut out the dead wood and the oldest stems?

Yes you can, but leaving about 6 inches of the stems from the ground for new branches will let them regrow a little faster.

20 years ago I was given 8 or 9 near dead Ninebark plants in pots from a nursery. I brought them back to life and planted 2 summer wine in the back and 2 Crimson Diablo in the front next to the house.

The summer wine ended up looking like yours so I cut them flush to the ground. They both regrew quickly but one I could kill by continuously mowing over it, the other I couldn't mow and had to dig up the roots to stop it from regrowing. they are hard to kill.

the Crimsons are better looking ninebarks but after cutting both to the ground twice they grew back just fine. I finally had to dig out the roots to kill one of them and and the other is still growing to this day. It had 3 trims to the ground so far, and because it's now taller than I want another cutting to the ground will happen this year. This is the best way to deal with ninebarks IMO, pruning and trying to shape them have a negative effect on how they look.

I've tried trimming, pruning and topping branches but they came back with a vengeance growing wicked and weird so the best approach is taking them to the ground.

"Topping" ninebarks will certainly make them grown "wicked and weird."