Our household has been coming at it from our understanding of physics, and have been since at least the 90s. It means that we’ve been watching through that lens for a very long time.
Without it, the episodes in Voyager where Harry Kim or Janeway came back to correct the timeline are meaningless. We would just assume that the unchanged timeline went forward offscreen.
This resilient river of time version offers a continuity where actions matter, and corrections to the timeline mean something more than just a shift in point of view.
As you note, multiple universes can exist but it takes something very large to do it. In Star Trek, we’re not in the infinite and ever expanding continuum of branching universes where every possible permutation of events exists. (And that version of the multiverse doesn’t stand up for hard scientists.)
So far we know that the Mirror Universe has different physics of light - something that’s so enormous that it’s hard to credit that it’s developed in any kind of parallel. It suggests some fixed events in the past development of the two universes that are extraordinarily resilient against branching.
The Romulan supernova is a major event but of a much lower order of magnitude than say the establishment of the physics of light. It seems like that would be a kind of lower bound for a branching trigger.
All to say that I agree that a Daystrom Institute deep dive would be worthwhile. In fact, it may be possible to go through onscreen canon and itemize the various events and inconsistencies that support this construct.