As noted in [0], locking or atomics are not required for merging
requests for a single mesh, because there is no multithreaded iteration
over objects that will process the same mesh in multiple threads. This
locking was added preemptively over the years and has made code
needlessly complicated, even while the final design for parallel object
iteration isn't completely clear. This PR removes the locks to simplify
some changes necessary for mesh attribute storage refactors.
[0]: b6764e77ef
Pull Request: https://projects.blender.org/blender/blender/pulls/141405