Top Gun was a legacy sequel to a beloved hit film from people's childhood. Hate to break it to folks, but ST09 was never a beloved hit film nor were either of the sequels. They were moderate successes that were viewed as fun trip to the movies and nothing more. Except for Beyond which actually failed. It's also still far too soon for the idea of a legacy sequel to be even remotely worth trying and the fact that multiple sequels already exist (with no more recent version having ever taken the spotlight from them) also undermines the sense of 'specialness' that makes a legacy sequel work. Plus, if the day ever does come, it still won't really be 'Star Trek 4' as it would almost certainly be missing half the cast (or more). That's par for the course with legacy sequels.
It is true that the problem is the budget. They gave these movies ridiculous budgets thinking they would be major contenders at the box office but they were consistently overshadowed by superheroes, dinosaurs and Jedi and by the third film the bottom just fell out completely. Giving a similar budget under these circumstances would be outright irresponsible. But there's not actually that much to be done about that. The Kelvin cast are -on average- vastly more expensive than any other Star Trek cast. And while you can try to pare down the cgi costs, the first three films established a pretty strong expectation of spectacle. There's really no good reason to believe general audiences would respond favorably to a new Kelvin movie that doesn't even try to deliver the spectacle they expect.
As for Star Trek being the fresh air people want as they turn away from superhero movies, that's really wishful thinking. Space adventure movies have been struggling longer than superhero movies. The fresh air people are turning to now is mostly video game and toy adaptations, and to a lesser extent movies that have an old school feel (old school as in 80s and 90s, not 2009). And regardless, it's already too late for that anyway. A hypothetical Trek film greenlit today won't hit theaters until 2027, maybe even 2028. And every day that passes without a green light that hypothetical release date gets pushed farther and farther into the future. The window of opportunity to define 'the next big genre' isn't going to stay open forever.
Also, just FYI, DC has officially completely abandoned their practice of keeping tv at a distance in favor of now having tv, animation and even video games all take place in the DCU movie world (with only a handful of exceptions).