Sort of, IMHO. Captain Atom, Nightshade, Peacemaker and even Judo Master have a history as being government agents. However, others like Blue Beetle (Ted Kord) are actually independent agents. Kord is a successful industrialist and inventor. The way I see it, he wouldn't need nor want to work for the government. And the Question is as anti-establishment as they come. Plus, even amping up their abilities, putting them at their peak (and I have MANY ideas on that front), I still don't think they'd be quite up to JLA level. I remember a L.A.W. six issue mini-series that came out a couple of decades ago by Dick Giordano and Bob Layton in which the fate of the Earth stands on the shoulders of the Charlston Heroes, and they basically have to take Captain Atom out of the board in the first issue, so he wouldn't overshadow the other heroes. On the other hand, I did think the Sentinels of Justice one-shot by Americomics (I think) did look pretty cool.
Peace
"Never assign to malice what is adequately explained by stupidity or ignorance."
"Great stories will always return to their original forms"
"Nobody is more dangerous than he who imagines himself pure in heart; for his purity, by definition, is unassailable." James Baldwin
Captain Atom: Team leader who treats the group as though it's a military force and he's the First Sgt.
PeaceMaker: Government stooge, bit of an idiot, backs Captain Atom 100% even though they don't like each other.
Strange Visitor: Honestly, I'm mostly including her because I love the costume, and I can see the government wanting somebody to be their "Superman" for PR purposes.
Powergirl: Doesn't take this seriously, is mostly just there to keep an eye on things and make sure the team doesn't do anything too shaddy or target the rest of the heroes
Patriot: A major powerhouse and embodiment of the Will of the American People... doesn't always line up with what the government wants.
Major Disaster: Minor thug and supervillian that turned good. Is able to handle the "gray areas" better than most of his team.
Black Vulcan: Much smarter and better than playing government games than most people expect. Is equally happy to play the part of the cliche black guy when it amuses him.
Tarantula: A vigilante that we're watching slowly go down a darker path
Sumo the Samurai: A nearly 7foot tall Japanese patriot from WWII that was trained in by a legendary martial arts master and give a potion of power, essentially a Japanese Captain America. He's been gone for a while, but now he's back.
Satan Girl: The creepy magic girl of the team
Director Bones: The government official in charge of the team. Comes off a lot more creepy and corrupt than he actually is. He's always accompanied by a non-de-script assistant who is really ...
The Unknown Soldier: Perhaps the actual real leader of the team
Someone already mentioned the JL Task Force from the 90's. This New 52 team was similar:
https://dc.fandom.com/wiki/Justice_L..._(Prime_Earth)
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Well, there always have been that element where you had a) the hero that is on the team to keep it honest, and, b) the hero who is rogue, but uses his "former" government connections for the greater good. I am glad that you mention LAW, which is what I was going for. WATCHMEN was also mentioned. But, there are indeed other government-sponsored heroes to draw from as well.