Mass dissolving of quads into a single point I have created a mesh via sculpting, then converted all of the resulting tris into quads. However, it left me with a less-than-ideal overall layout.

The problem, as you can see, is that while most of the mesh is constructed from perfect rectangular quads in the exact layout that I'd like, but every so often there's an "odd one out" sort of situation.

I know exactly how I'd like to go about solving this problem. If a single vertex were to be created in the middle of each of these twisted quads, as I've manually done to this one:

Then this entire issue would simply vanish. However, this is a 10,000-polycount mesh; I'd prefer not to have to manually do this for every single repeat of this issue.

So, my question is: does Blender happen to have any methods, perhaps a setting for a modifier or something, that would be able to en-masse collapse these broken quads in the method I described or something similar?
You can try to use the Decimate modifier, but to get clean topology, I am afraid you will have to do it manually, consider a complete retopology of your sculpture. If you decide to fix your mesh, you can speed up the merging process that batFINGER posted in the comments, by using Shift+R you can repeat the last action, thus reducing one step of the merging process. Which normally you will have to press Alt+M and then "Merge at Center", with this you only do it once, and next time it's just Shift+R.



The decimate modifier could get you some results quick, but you will have to keep an eye out for your topology, if you decide to use this method. Keep in mind that it may decimate already good topology you had. Also experiment with the three modes decimate has, "Collapse", "Un-Subdivide" and "Planar".