Well, I understand the sentiment, but unfortunately there are myriad situations where that is the ONLY remedy, and many of them would SEEM to be lesser issues, except that even after many weeks or even months of chasing ghosts that ends up being the only option.
Reasons? F. I dunno, I just know that it ends up that way more often than not. But certainly it's worth TRYING to continue to find other options if you have the time and inclination to do so. Perhaps it IS something related to a recent Windows update, etc. And PERHAPS there is a less intrusive solution to the problem. I don't know that either. What I DO know is that YOUR case is the first one I've heard of in regard to the disappearing Windows media player and what I DO know is that more often than not when somebody has come here with a "one off" problem, the only resolution typically has been a clean install.
Now, if you want to try, you could certainly investigate the possibility of downloading a Windows media player installer as well as a Media feature pack installer, if they can still be found. No guarantees there because sources for those have been disappearing for years now, but maybe you already have the MFP installer at the least. It's certainly worth a try but if that isn't an instant remedy or even possible, then a clean install will absolutely be the most expedient remedy, bar none. Aside of course from having to reinstall your programs and set your preferences back up, but the fact that you still have access to the OS and this is not a no-boot situation might alleviate SOME of the pain of that.
The only other option I can think of, and it's an unlikely remedy because I doubt the problem is related, is perhaps to try using the DISM /Online /Cleanup-Image /RestoreHealth procedure followed by an SFC Scannow, and maybe the problem is merely a file system bork, but I'm doubtful of that.
Perhaps others might have better insights, it certainly happens from time to time, but again, I'm not terribly hopeful because this definitely seems more like a one off type situation to me. And those do happen, for whatever reason.
Also, I've invited some other very skilled members to chime in here in case they have better ideas than I do. And that too, happens.