I think my issue with the idea of a Monsterverse is that, unlike with the Marvel films, whatever happens ultimately has no lasting impact on the titular characters. There are definitely Marvel films that fit that bill, but overall they have a progression to follow and a common goal to accomplish. The resulting Avengers Endgame was a film featuring dozens of characters who all had arcs, progression and motivations.
Contrast that to a monsterverse in which the bread and butter of the plot is "Who is fighting who?" and nothing else. Godzilla was the same being in the second film as he was in the first, and will continue to be in any following films. Contrast that to, say, Thor of the Marvel universe who begins life as a cocky prince who can't wait to be king and has ended his latest appearance by willingly giving up the throne after having matured into a wise and caring ruler.
The marvel films certainly have plenty of issues and are oversaturated to the point of absurdity now. I'm not trying to raise them up as shining examples, rather using them to show how I don't feel a monsterverse will ever be as compelling for anything other than action. Although I never liked the Captain America films, I enjoyed seeing his story come to an end in Endgame. It felt human and important. I'm not sure I'll ever get that in the likes of a Godzilla or a Kong.
It's that that makes me wish they were taking a more disconnected approach to the monster films. Occasional crossovers, yeah sure. Kong V Godzilla had to happen. I just can't see myself being drawn into a universe in which the main characters are just continually roaring and gearing up for the next fight. I feel it cheapens the sheer spectacle, and I'd much rather the filmmakers concentrate on the grandeur of these beasts individually rather than tying to tie them all up into one package.
That said, I'll still likely watch them all. I think it will just be more of a blow if there's a bad film as I'll know I'm forever locked into that continuity and can't escape it if I want to watch the films that follow it.