There's a few issues and I think some of has to to do with philosophy and formula... but I'm gonna state something now that might not be popular.
Demario Davis is not playing well. He does not look like the same player.
Understanding how unpopular this take will be, I'm gonna include some film (apologies in advance, I'm pulling from the broadcast in espanol b/c the NFL doesn't let you clip videos).
Here is Davis blowing an early assignment in coverage. The are in a 3-fire look (cover 3 with a 5 man pressure). Harris spins down to take that curl/flat/hot-to-2 responsibility. Davis is what we call the RAT--his job is to take away shallows, digs, and posts. The Chiefs do a great job formationally here with the delayed release by #3 to the flat, but even still, Harris should be passing off 2 and taking 3/playing curl/flat (which he does) and Davis should be sticking to his rat responsibility. Instead he expands and the middle of the field is wide open for an explosive play.
Here he is on the same drive, blowing another coverage assignment. The Saints are in man, which you can see right away with Taylor traveling with the motion. At the snap they sift Worthy behind the line for the backside flat route. Lattimore does the right thing and sticks with him the whole way. In no situation is Davis manned up on Worthy, yet he expands with him and gives up the delayed checkdown (to the TE)--which is literally his first responsibility.
This may be one of his most frustrating plays, as he comes through untouched on the blitz, with Mahomes dead to rights, and just misses him in a incredibly poor attempt at tackle.
I know the question is about run defense, and both in this game and the Eagles game, Davis was seriously lacking in that area too (a horribly missed fit/slow reaction by him was what gave up Barkley's long TD run). Obviously Demario Davis has earned himself some grace with how amazing he's been to the team over the years...
But, bluntly speaking, he is part of the problem right now. I'm sure some of it is injury, but those blown assignments are a result of freelancing and undisciplined play. It's so uncharacteristic of him that I am wondering if maybe Allen is asking him to do certain things, and yes--some of those plays were very well-designed and maybe the defense just wasn't prepared for them.
It's not the only thing ailing the Saints' defense, but Davis's screw-ups are really standing out right now, especially without Pete Werner on the field (who, conversely, is one of the most disciplined, assignment-sound players on the team). I hope that he can turn it around, because the defense and the team depend on him.