Will my trees recover from bad pruning?

Oh, my. It looks like a tree trimmer has repeatedly visited your neighborhood to "prune" the trees, not just your trees, but also those of your neighbors.

The method that was used is a variation of topping, sometime referred to as a "round over." Unfortunately, that sort of pruning is rarely, if ever, recommended by well-trained arborists. (See Don't Top Trees!)

The outcome of cutting off the top of a tree or, in your case, across a relatively large branch, is as shown the illustration in Tree Pruning on page 3, at the lower left. The new shoots that arise near the cut are loosely connected. Thus, once they become large enough, they will break loose and drop without warning.

I've taken your image and marked to show where the tree was pruned at least 3 successive times, first with the white line, then a year or two latter at the green line, and a 3rd time at the gray line. Notice that an errant branch just right of center at the top escaped being cut as short as adjacent branches.
(The red arrows point to similar, poorly pruned trees across the street!)

The preferred remedy would be to hire a Certified Arborist to repair the damage by removing excess branches and shortening others. A corrective project such as that is likely to require 3 years or so with the goal of returning the trees to a normal growth pattern. Restoring Topped Trees describes the process.

You can locate nearby Certified Arborists by searching with your zip code at Trees are Good - Find an Arborist. (We suggest Certified Arborists because they must pass an exam to obtain a license, then must acquire Continuing Education Credits every 2 years.) Many Certified Arborists in the metro region serve all 3 counties, Clackamas, Multnomah, and Washington.

Call at least 3 companies, and make certain the company you choose understands the project. For instance, many companies keep a photo collection of before-and-after images that will display prior projects they have completed.