Yes the Corre have broken up, although Gabriel and Slater are staying a team for now.
The biggest problem with the tag division is that there's absolutely no longevity to these teams. It's like whoever is behind the scenes controlling this shit sees a team with some charisma and breaks 'em up thinking it'll translate into single's wrestling charisma... and it doesn't, and you lose 2 more guys to Superstars and have them taken off TV completely.
Show & Kane's run ended WAY too early, even if they HAD to fill in someone to feud with Del Rio... it still looks like they're going to use Show less and less right now. IDK why Del Rio couldn't feud with R-Truth, or Miz (if you wanted to make Miz a babyface).
Then you have these factions, who you don't give the titles too... or you give it to them and never have them defend... or they don't hold the fucking belts for long. If a team had the belts for a 3-month run and ran through every team possible and actually have a tag-team tournament for #1 contenders or something along those lines, you'd start to build prestige back up. The E just doesn't fucking care about making a star TEAM, they just want to find their next star, period.