Make a situation with some utterly despicable entity, but give a reason that the military CAN'T take them out, like a diplomatic immunity or something that makes it clear that this is something that tanks and helicopters can't do
because they're not allowed to, not because they're incapable. That's why you have a squad like this that's completely expendable from a political/military standpoint with no ties back to who sent them. (The first thing Enchantress does in the film is about the only thing that meets that qualification really, REALLY well).
You can have your key villain as someone who's a figurehead with a big taskforce protecting them like Lex Luthor or Ra's Al Ghul who the government can't directly attack over issues of diplomatic immunity or public international relations, who's still going to need crazy force to take down, and still get the "use bad to defeat evil" angle. While the Suicide Squad are a team of very powerful freaks and metahumans – they're not there to do a job because they're a superior force to using the military, because they're not supposed to be that whatsoever. They're there to kill someone as ordered by the government/military, but in a way that's completely off the books.
tl;dr — The film's villain needed to be someone far too dangerous for the government/military to leave alive, but simultaneously someone they had ZERO ways of dealing with eliminating them legally. They're there to use them like Navy SEALS that, if the mission goes tits up, you can just say, "Welp, looks like all these terrible people just went at each other over a bad deal." —
which is also the same thing you say if the mission goes as planned. They never get to be heroes.
The situation in the film is DEFINITELY not that.
X