@jwz It would be better if it worked the way you described.
I think the reason we got where we are is that the Fediverse fell into a pattern of making Open Source replacements for proprietary social network services. So, Mastodon is the Twitter replacement, Pixelfed is the Instagram replacement, Peertube is the YouTube replacement, Lemmy is the Reddit replacement.
I think the way out is for more of them to give you the option of acting either as their own server, or as an ActivityPub client.