@jaybate-1.0 That we can do! On the transfers, I think it is due to some players having more options after playing elsewhere than they did when graduating from HS. They might have been under-recruited because of poor exposure by not being AAU participants, they might have had unpolished skills due to inadequate HS coaching, they might have been immature and not handled recruiting well, they might have made an initial college choice based on non-basketball reasons like friends or family, they might just have gotten better...a myriad of reasons.
Why Self would want them is exactly as he says, to fit a need. He fills holes. I think he may appear to be taking kids from programs in the 30 to 200 rankings not from desperation but because those are precisely the ones who may be seen as able to move up to more elite schools.
With transfers who sit out, like the Lawsons, he gets monster practice players who can only improve while improving the eligibles. With graduate transfers, he fills an immediate gap with no long term risk.
Consider something else: where did all the KU's transfers who have left gone? Did they go to other blue bloods? Or, as I propose, do they generally go to secondary level schools?
I cannot vouch for the accuracy of my observations, but it seems there are very few top-tier players transferring between blue bloods. And there are very few really good players or starters transferring out of blue bloods in general. Good players move up to play at more elite schools, bench players move down to get more playing time.