Nah the Suicide Squad hasn’t done any actual black ops stuff in a while, and they’ve got a different vibe. They’re supervillains forced to work for the government not willing agents, if that sounds too similar to the WildCats for you, than the Titans are too similar to the JL and shouldn’t exist either since both just fight supervillains. Plus the traditional SS doesn’t even EXIST currently.
Checkmate doesn’t DO anything, Bendis tried to make them work but that failed, that organization is irrelevant these days. What we need is a book that defines all the other government agencies in an understandable hierarchy. You have the Wildcats and the Suicide Squad with clear cut boundaries, and the Wildcats should be going up against other government metahuman black ops, basically make the Wildcats part of a metahuman arms race between nations, the superhero as a political thriller essentially. They’re the government’s first resort with the SS being the last resort.