I think it would be stupid to move STARGIRL to Earth-Prime where THE FLASH and others are set, since there's a different Flash on her world. If they had to amalgamate the continuities, we could lose some of the Justice Society of either Earths. Hindsight is 20/20, but maybe they should have left BLACK LIGHTNING on his own Earth--which could be STARGIRL's Earth-2--so those shows could cross over, as they're both filmed in Atlanta, although they are aimed at very different audiences.
What I think most fans meant about the Arrowverse is that certains shows were spun off from ARROW. But that really only applies to the shows that were developed for the CW. They all owe their existence to ARROW's success. But SUPERGIRL, BLACK LIGHTNING and STARGIRL were developed for other platforms--they've just ended up by dumb luck on the CW.
And as I said before, forcing Arrowverse to mean everything--all of the Multiverses--I don't think that's in the spirit of what fans first intended with that term.
To be fair to Supergirl- I'm not sure if it was originally developed for them, but it was offered to the CW first. They passed, not wanting (at the time) to become known as DCTV. It was only after it premiered that they regretted passing on it, and they jumped to pick it up when it was cancelled by CBS.
And it worked for what was happening anyway, at least on Flash; discovering the whole multiverse thing.
Stargirl though... If it had been done before Crisis on Infinite Earths, it would have been more feasible to be on Earth 1, or at least as a potential crossover. But since that didn't happen, the multiverse will need to be "rediscovered" for it to make sense for a crossover.
Not to mention The Legends also met a different JSA and another Stargirl.
Although it would be fun if that Stargirl's cosmic staff popped up again in the present day. (I don't recall, but for all we know it should still be out there somewhere right?) Maybe it's what ultimately leads to the "Stargirl" crossover and a rediscovery of the multiverse? (that'd be a big enough event to warrant Jack Knight finally being used, imo )