The Greefs - My Three Sons
I still can hear there song “I’d Be A Good Man To Have Around The House”
I also liked the girls from Petticoat Junction
I clicked on your link, then re-read your post and thought it read “I’d go with the Rulers.” I was quite confused.
Just thought of another - Jet Screamer, from The Jetsons, with their top hit “Eep Opp Ork Ah Ah”
The Commitments
The Soggy Bottom Boys
I grew up with The Buggles, The Monkees, and The Partridge Family so they will always be my fav…
The Evolution Revolution From Lancelot Link
How has nobody else mentioned Citizen Dick?
Also, if we can include bands from comic strips - I’ll nominate Billy and the Boingers.
Barry Jive and the Uptown Five (f/k/a Sonic Death Monkey, a/k/a Kathleen Turner Overdrive) from High Fidelity.
Can’t forget The Kinky Wizards with their debut EP “I Sold My Mom’s Wheelchair.”
Drive Shaft, from Lost.
You all, every-butties…
A few links are in order.
Dingoes Ate My Baby from Buffy the Vampire Slayer
The Wonders (originally The Oneders) from That Thing You Do! Probably my favorite soundtrack album.
Fistpump from Regular Show. We don’t know what they sound like, but their logo and merch was great.
Camel Lips from John Water’s Serial Mom (really L7 in disguise)
Beef from Phantom of the Paradise
Löded Diper from the Diary of a Wimpy Kid books (and movie). Actually, they sound pretty bad, but the name and logo are great.
Sure are!
And a few more:
Commitments:
The Soggy Bottom Boys only had the one real hit, but it’s a good ‘un. My affection for them stems as much from their adventurin’ and misdemeanorin’ as it does for their music.
Strange Fruit from “Still Crazy.”
The Scum of the Earth, a British band from an episode of WKRP in Cincinnati.
“We’re not punk rock. We’re hoodlum rock, several steps below punk rock. The difference is that punk-rock groups dress deplorably, and they do not physically attack their audiences.”
The band from the Mos Elisley Cantina, of course!
That wasn’t a fake band. 
The band with two lead singers/guitarists in one! Bang Bang from Brothers of The Head.
The Mosquitos from Gilligan’s Island - Bingo, Bango, Bongo and Irving