There's no more need for the universe to be shared concurrently than it is consecutively. If each writer is telling new Spider-man stories they can just as well tell new Fantastic Four stories. If they're not bound by what happened in a past Fantastic Four comic why should they be bound by what is happening in a Fantastic Four comic that just happens to be published in the same month? (It would make matters a lot easier for people writing the Avengers if they didn't have to care what was going on in anyone's solo titles.)
You're already contending that there should be no reason for readers to check out the back catalogue other than the intrinsic merit of any particular story.
You're already contending that Spider-man's universe effectively reboots every time the writer changes with no risk of diminishing returns.
It's rebooted itself at least twice since the new series started. As you say, it's only technically the same continuity. There's essentially been a hard reboot between each showrunner, and arguably there was another reboot for the final series of the Twelfth Doctor. But Doctor Who doesn't have a shared universe, and it necessarily has to cope with the fact that actors move on.It would be easier to reboot Doctor Who. And that would be a bad idea too.
(I think you probably missed my questions about the Doctor's granddaughter and Uncle Ben, since I only added them when I edited my post.)