If big pizza franchises wanted HPOP they could just make it the api by which their apps talk to their backend. New cross-pizza-place-apps and tools would pop up within a month
Really, they could each do their own bespoke thing as long as they didn't go out of their way to shut out other implementers.
Instant messaging used to work like this until everyone wanted to own their customer bases and lock them in, for the time-wasting aspect
That would require them and there random IT teams to get together, sit down, agree on doing this, design a common protocol, etc. - that's enough friction to make it not happen, especially given the lack of reward.
With AI browsers, all they have to do initially is not break them, and long term, each of them can individually choose to offer their API - no coordination required - and gain a slight advantage.