I don't see how it would be costly to get clearances given that they're all DC/Warner Properties
For one thing, actors get paid residuals for reuse of footage that they're in. The more actors whose faces they showed, the more money they'd have to dish out. For another, WB isn't always the exclusive production partner in these things. The reason it was hard to arrange the
Supergirl/Flash crossover last season is because the networks had to negotiate certain rights and financial matters between them. I'm sure the same would go for getting clearance to use footage from a FOX or NBC show on a CW show. After all, those networks are competitors. Warner Bros. might be happy to tie the shows together, but they aren't the only ones with a say in the decision, and the networks might be more reluctant to help out the competition without getting something in return. As for movie footage, the movie and TV divisions of WB are separate companies, despite being owned by the same conglomerate. They aren't automatically on the same page; in fact, they seem quite disconnected and often have conflicting interests.
Whilst I admit there are certain story possibilities that might be fun to explore with Earth's-1 & 38 remaining separate - a few pages back I suggested a 'Prisoner of Zenda' style Supergirl episode involving Earth-1 Oliver posing as Earth-38 Oliver who's still a sex-obsessed douche on Supergirl's Earth, and there would definitely be some comedy gold to be had from Diggle visiting the alien bar (not to mention Cisco, Felicity or Ray drawing comparisons with the Mos Eisley Cantina) - I would still prefer those two universes to merge.
It's not just about individual story possibilities, it's about the character and history of the separate worlds, which is what makes alternate realities interesting. I like the contrast between a world that's still getting used to the novelty of metahumans and aliens and a world that's had a substantial alien presence shaping it for over a dozen years. It gives them distinct cultures and attitudes and allows for quite different story possibilities. For instance, "Invasion!" could never have happened on Earth-38; an alien incursion would not have been the catalyst for an unprecedented team-up of heroes, because the DEO would already have been in place to deal with such things, and Superman's probably already dealt with a number of alien invasions all by himself. And
Supergirl's stories this season using alien immigration and amnesty as real-world allegory obviously couldn't be told on a world that's had very little contact with aliens.
You listed above a number of ways that the two can be linked whilst being separate, but to me it's still contrived. It's way simpler if you want the characters to interact if they can just walk down the road, instead of walk down the road and have to use some contrived device or metahuman as well to do so.
It would be enormously more contrived to rewrite the entire histories and backstories of the worlds and their characters in order to arbitrarily force them together. Besides, the multiverse has been part of the DC narrative (and particularly
The Flash) for most of the past 55 years. So including stories about the multiverse is no more contrived within the context of a DC show than including stories about the Speed Force or Lazarus Pits or aliens with levitation and heat vision. Or, for that matter, masked vigilantes who routinely break the law and even kill people while the authorities look the other way and treat them as "auxiliary law enforcement." The entire concept of superheroes is contrived.
As for simple, it'd be simpler for Bruce Wayne to spend his billions funding anti-crime programs and domain awareness and infrastructure repair and social services, rather than trying to fight crime by punching criminals one at a time. It's not about what's simple, it's about what makes for interesting stories. Parallel realities interacting and exploring the differences between their histories and cultures is interesting. It's one of the many science fiction tropes that superhero comics have wholeheartedly embraced, and I don't see the value of getting rid of it, any more than getting rid of time travel or telepathy or aliens would be a good idea.
And lets not forget that it has caused one or two problems such as Linda Carter not being made president on Earth-1, because the producers thought people would get confused.
I don't see that as a problem. It's just an idea they tossed out and decided not to go with because it wasn't practical. That's how creativity works -- you consider a bunch of ideas, use the ones that work, and reject the ones that don't. It's not a breakdown of the process if a single idea doesn't pan out, because it's just one of many that are tried out in the course of figuring out what works. It just got more attention in the press because it involved a celebrity. But it would've just been a cameo scene in one episode, so it wasn't that big a deal. There's a big difference between what gets a lot of press and what's actually important.