Any reason we cannot have that kind of feed with the current tools and general pubs? (Sorry if it's a trivial question, I'm new.)

Not really! You could do it with the current protocol, it could be implemented as just a custom feed algorithm.

A really simple version could go like this:
a client extracts any hashtags listed in the pub’s bio, and constructs a feed of all posts from anyone who is friends with the pub that use the given hashtag.

If you want the pub to feel more like its own space you could use a different message type. Like community-post instead of post. Then it wouldn’t show up in most existing feed algorithms.

There was some pushback to tying groups to pubs, which I understand, although tying a group to a pub’s identity instead of its DNS name doesn’t seem so bad to me. Especially since no one is working on the private groups implementation anymore.