That's the thing, though -- as the aftermath of Crisis on Infinite Earths in the comics showed, the very act of merging multiple continuities into one was a humongous contrivance and it added far more complications than it was intended to remove. Rewriting multiple contradictory histories into one is a hugely complicated exercise that requires taking every possible factor of the different universes into account and finding ways to reconcile them. Any contradictions that are missed can create major complications that need to be later reconciled with even more complicated contrivances and handwaves (e.g. the "pocket universe" that explained how Legion of Super Heroes could keep using Superboy post-Crisis even though Superboy was no longer a part of Superman's backstory). And trying to rewrite characters' backstories for new continuities can lead to all sorts of convolutions that end up making them messier rather than neater (cf. Power Girl).
So if your goal is to minimize contrivance, then merging the universes is a cure that's immensely worse than the disease. Sure, if the shows had been set in a single, consistent universe to begin with, that would've been simpler. But trying to rewrite two separate universes' histories into a single one after the fact is anything but simple. In the comics, it created more problems than it solved, and I'm sure it would on TV as well.