Once again a non-sense no value adding issue to kill a function. Why? Why the whole discussion, wasted man-hours? The suggested alternative hook_module_implements_alter is not a replacement, you cannot have control of the module weights/
Please re-read TR's comment #2968232-6: Deprecate module_set_weight() → . He listed imported use cases.
I'm not convinced that this function should be removed. I also don't see any reason. Why remove something that doesn't break anything, only to break things?
I'm having the same problem on cron or updates. I have a hook_cron implementation which daily updates user's with some specific criteria. Those users' realnames are broken. The same problem occurs if I write a hook_update_N implementation to a module and run the updates via drush.
The patch at #439 works very well on Drupal 8.8.11.