Lots of possible uses for private games, beyond the obvious. Off the top of my head: when working on mods I'll relaunch a game dozens of times and Steam will spam the in-game notification to my friends unless I sign out of chat. Now I can stay in chat and just make the game private until I'm done modding. Some games get left open a lot (like idle games) and I don't want them cluttering my profile's recent games. Sometimes I just want a dumb-fun game without advertising it to friends because I'm self-conscious about it. Some people have coworkers as friends on Steam so they can play socially, but some games may give away political/personal information that they would rather keep private (eg, LGBTQ+ focused games). I have young family members who are friends on Steam and I'd rather they don't see certain games in my library.

I wish it was implemented like an access control list instead of just private or not-private, but being able to keep the games I want to play with others public and keep other games private is absolutely brilliant. Now I can take private mode off, which makes figuring out which game to play with friends much easier since they can see my library and the "what games do we both have" library filter will work.