Correct Face Attributes (UV) should be utilized by all edit mode tools and operations.

For example, as I'm trying to clean up some messy geometry from Google maps, I want to merge 700 unnecessary points down to 1 point without changing the UVs.

If I activate Correct Face Attributes along with Auto Merge Vertices, I can select all of the points and scale them to zero. They will be merged to a single vert and the UV'd texture will look the same.

However, If I use Merge At Center, the UVs will change and the texture will look wrong. Scaling to zero and merging at center are practically the same operation. Correct Face Attributes should work for both.

If I activate snapping along with Correct Face Attributes along with Auto Merge Vertices, select all but 1 of the points, scale to zero, then snap that merged point onto the last point, I get the same result as using Merge At Last except the UVs don't get broken.

There is no UV conserving workaround for Randomize Vertices or Smooth Vertices so I've been having to extract a portion of the object, duplicate it, smooth vertices, and then manually move verts on the original object to match the smoothed object.