Great article about the psychology of push-ups! In my experience "knee-ups" (6-point push-ups) fail to teach proper technique... and don't help with the mental stumbling block. I've found a better regression to be incline push-ups with hands on the wall or a couch, for example. That teaches the abdominal tightness necessary for a push-up instead of substituting the hip flexors and lumbar extensors.

Another great regression is simply a "high plank" (plank with elbows extended). You can turn it into a push-up eccentric by trying to lower yourself as slowly as possible from the high plank, and then bringing one knee up to catch yourself. Again, it's much more specific to the push-up than a push-up performed on your knees.

Here's the mirror article for pull-ups in Elemental https://elemental.medium.com/your-inability-to-do-pullups-is-all-in-your-head-191278c2f5aa