PieFed already has that, in "Categories" of communities. If you select gaming, it combines all the posts from all the communities that are related to gaming. I'm not sure how it works, maybe each instance admin has a list somewhere.

Furthermore, an individual user is subscribed to all of those, so that you can easily remove content from certain communities merely by leaving it. Or join more of them.

~~I think Mbin has something like this too, though at a casual glance without a login I cannot see it.~~

Lemmy is starting to fall behind these other alternatives, written in more commonly used languages (than Rust) so allowing contributions from more people, which helps them gain features more quickly.

Edit: and to address the issue of forgetting what community someone is viewing, that's not an issue either: every single post includes the entire community description at the bottom of it, beneath the comments - here's some examples: a post with few comments to have to scroll past, another example showing a YouTube preview (also offers direct piped.video link), here's a non-gaming example of a post I made that includes #hashtags at the bottom. In all of those see the categories up at the top, and in the former two on Beehaw, the special note just below the post about how that instance has different moderation practices than usual, with a direct link to what those are, in the admins' own words.

Overall PieFed lacks some polish compared to Lemmy, especially in replying to comments more deeply embedded in the threaded conversations of larger posts, yet in so many ways it already has surpassed what Lemmy chooses to offer its users, it's fantastic to look at, and even more exciting to think about where it will head next!:-)