Services will simply offer their data with an API (and micro-transactions to use it), and then 3rd parties will create UI's for each interface.
Tweets are a useful data type, but there's nothing about twitter's brand UI that is necessary.
We could have this right now if iOS, Android, TVs, Windows, macOS, Linux, etc. all used HTML+CSS instead of their own toolkits. Yet they don't. Creating some fancy alternative is an even harder problem, since (a) that alternative needs to be designed and built and (b) all those same platforms will still need to switch, except we would also have to switch over the Web too.
This is a political issue, not a technology issue: it requires convincing a whole bunch of organisations to perform a costly change, for little direct benefit to them.
This would also be very easy to abuse via "embrace, extend, extinguish". Consider the history of word processors: everyone used the de facto standard (Lotus Notes) for compatibility. When Rich Text Format came along, underdogs like Word could read and write Notes-compatible documents. Once Word's market share rose, Microsoft "extended" the format so its documents could no longer be read reliably by Notes. Customers then switched to Word since it was "more reliable" at reading documents (i.e. it could handle the valid files produced by Notes, as well as the broken junk that Word produced).
Of course, Microsoft tried the same thing with HTML (badges like "Best viewed in Internet Explorer" became common precisely because IE did things in an incompatible way; I remember the relief among Web devs when IE7 came out, at its slight move towards compatibility!)
The current dominance of HTTP is largely due to firewalls, NAT, and possibly developer familiarity (e.g. proxying, debugging via cURL, etc.).
I wasn't online in the 80s, but I remember networking in the 90s being a mixture of HTTP, POP, SMTP, IRC, FTP, Telnet, NNTP, etc. The noughties saw an increase in protocols for P2P, instant messengers, etc. These days those seem to have consolidated (e.g. BitTorrent, XMPP, etc.), are often tunneled through HTTP, or are displaced by something newer which tends to use HTTP.
Then when I start thinking about what that would mean I realize it's almost always going to be an evolution not a revolution for the following reasons...
1) No one wants to deliver two UIs, one for HTML legacy browsers, and one for the hot new browser rendering.
2) Who would own the standards? If it's a consortium we'll be back to lengthy RFPs and glacier pace of agreement, possibly resulting in something worse than HTML that does not get adopted. I can't see how any one organization could own the standard and get other browser developers to buy into it.
HTML+CSS is so integral to everyday life it's hard to see how it could ever be deprecated.