Specifically, and I'm not sure if it's just me or anything, but I think there should be two rules when it comes to make an opening for a show. Probably not official (because that would be stupid and Congress has other important work to get in a deadlock about), but at least a de-facto practice.
For one, I want theme songs to stop just having everyone chant the name of the song. It's very tempting and I'll be honest when I'm alone I like to sing songs I like while replacing all the lyrics to just be the name of the show or a character on it, but that's more along the lines of a dorky, guilty pleasure I do so I have a vice that isn't, say, designing deathtraps.
Granted, I understand why some people include the name of the show in the theme song. Theme songs, or at least the best of them, actually live up to their name. They convey the themes of the show and the mood of it. There are quite a few that rank up as my favorite theme songs (Lupin III's opening most notably, which gets a free pass because the melody of the song captures the feelings if high-profile heists better than any song lyrics and they don't actually say the title more than a few times) but too often it feels like an insult. Like the executives are afraid that we're going to forget about the name of the show so they hammer it into us relentlessly at the price of anything else. And if it's not the title that gets spammed within the opening, it's some trite catchphrase that is rarely as popular as said executives hope it will be.
The other problem that bothers me goes along with this: where the theme song is supposed to fill us in on the entire backstory of the plot and how everyone got to where they are. It's not like an origin story for the first episode is that hard. Or better yet, simply give us a narrator to briefly fill us in on the situation before the actual story starts. Works just as well, if not better since you don't have to go at a breakneck pace to fit all that exposition into a minute-long opening.
I dunno, maybe I'm just being a cynical moron but I've seen theme songs that are genuinely beautiful pieces of music and the best of the best do their own thing. Biggest example being Casshern Sins's.
It tells us absolutely nothing about the plot, the animation in it is practically nonexistent, it never mentions our hero Casshern's name, and it's frankly one of my favorite songs ever. It conveys a kind of tragic feeling to it which fits in well with the nature of the show and I can't think that replacing every other lyric with something like "HIS NAME'S CASSHERN!" would do anything except ruin it.