I think it is a choice between the two, in some respects. A studio has finite resources, and writers and other creatives have finite time and energy.
Warner Bros. is making a Joker film that's out of continuity with its other DC films, as well as several mutually incompatible television continuities -- the Arrowverse, the DC Universe streaming shows, and
Gotham. (And both the Arrowverse and DC Universe continuities are from Berlanti Productions.) If WB can pull that off, why can't CBS? After all, CBS Studios makes
plenty of other shows besides Star Trek as it is, which conclusively proves that it
is capable of working in multiple different continuities at once. For that matter, Warner Bros. produces a whole bunch of things besides DC. Really, the only single-universe studio I can think of is Marvel Studios. The norm is for a studio to produce many shows and films set in many different realities.
Not to mention that it would take pretty much the same amount of resources to make two Trek series in different realities as it would to make two Trek series in the same reality. The only thing that would make the latter more affordable is that it could reuse sets and materiel between shows, but only if they were in the same century, which will not be the case for all of the new Trek shows currently in production or development.
George Lucas did Star Wars because he couldn't get the rights to Flash Gordon. In a world where he was able to get the rights, there would have been no Star Wars.
But 20th Century Fox would still have made a ton of other movies. You were talking about a studio, not a single filmmaker. (For that matter, the existence of
Star Wars did not preclude the existence of Dino De Laurentiis's 1980
Flash Gordon movie.)