I think that this is artificial for most critics of Capers-- a bit of a straw man. While I'm sure there are people who want to scapegoat him, I along with many others have pointed out issues in BOTH personnel and schematic deployment/development. It's possible (and frankly, realistic) that the defensive issues stem from both sides. TT, despite being a stellar draft guy in the long view, has straight whiffed on occasion lately and exascerbated those misses by refusing to dip into free agency to make up for them. The defensive staff has not, in my opinion, done a great job of development and certainly doesn't scheme to to put players in a position to succeed.
I guess if you wanted to sum this up in two players, you have Damarious Randall who (though he may rebound) just doesn't look like a good pick at all. He's a finesse safety transitioned to corner who doesn't seem able to cut it. That's poor prospect evaluation and draft execution and falls in Thompson's lap.
Then you have Casey Hayward, a very talented cover corner who this defensive staff had pegged as a slot-only player. So they allowed him to leave and he went to San Diego, where he shadowed #1 received more than anyone in the league not named Patrick Peterson, allowing 1 TD and picking off 7 passes. QB's throwing into his coverage had a passer rating of about 50. The staff had an All-Pro talent on their hands and never knew it.
So it's both. And I think most informed fans are willing to see both issues. I think they ought to have fired Capers, but I also think that TT needs to change his approach (especially concerning FA) or get replaced himself. Furthermore, for everyone who wants to blame absolutely everything on Capers there is someone who wants to blame absolutely everything on Thompson, whether it's fair or not.
And finally, to clarify the Falcons situation (because I had the same read on the situation as you did initially), their DC was basically stripped of his duties at mid season by Quinn, which is when the defense began to improve. Quinn took on the defensive play calling himself. That's per Mike Lombardi of the Ringer. He said that the DC was going to be out at the end of the season no matter what happened because of the first half of the season, not because of the Super Bowl.