I was trying to understand the same. I found this summary helpful in listing what the fans are upset about:
Some issues do seem legitimate but as you said they have been mostly competitive over the time frame they are complaining about. Their expectation that LAG should be winning more championships because of their history comes off as entitled whining to me. I'm sure getting upstaged by LAFC hasn't helped. At some point, they need to come to terms with the fact that this isn't MLS 1.0 where they are the exclusive crown jewel of the league that will outspend everyone and has special rules made for them.
My cynical TLDR: Entitled fans base that has been coddled by the MLS for years can't come to grips with the idea that things have shifted and they have to compete on an even playing field now and as such they won't be winning a title every other year.