But that would be the wrong solution to the problem. I should be able to add whomever I want, and then be able to mute them permanently.

I think if you add not-friends to your friends list, the Algorithm(tm) perhaps justifiably recommends things from your friends list, and you get junk recommendations, the problem isn't entirely the Algorithm(tm)'s fault.

You feed the Algorithm(tm) garbage and it returns you garbage, and somehow it's all the Algorithm(tm)'s fault.

It's the algorithm's fault for not listening to my "mute this person". I had my feed muted so I didn't see any posts (which is how I wanted it), but now I see random "recommended" content, with no way I can see to opt out. That's not my fault.

This is like complaining that a blog site shows you blog posts. It's made for this purpose, not yours. Using it is your choice - don't.

FB has an entire team of very well paid people whose entire job is to tweak this algorithm. Presenting relevant content is the whole concept. I suspect where it goes wrong is chasing “engagement” at all costs despite whether it’s emotionally pleasant to the viewer. FB doesn’t care if I actually like the content they present - just whether it keeps me on the site longer. That is, I believe, a poor choice since, at least in my case, it led me to stop using their service.

Isn’t that what “unfollow” is on FB (stay “friends” but they don’t influence your feed)?

It is, but now it shows me random groups for me to "join" and there's no way to remove those.

They were people I was connected to as part of my line of trade.