Submitted for your consideration

Is Bill Self the top coach in KUMBB history?

If not for Phog, I would say yes.

If Bill wins another NC, maybe, but for those whose focus is national titles, Phog would still be +1 in NCs thanks to the Helms titles.
(Yeah, I know it's not the same as winning it on the court, but that didn't happen before 1939, so it is what it is, a title that was awarded by someone choosing the best since there was no national title game.)

If Bill wins at least 2 more NCs before putting down the clipboard, it will be hard to argue his status as the best, but Phog would still have to be considered the KU coach with the most impact on the history of the game. Shoot, Phog is arguably THE most influential coach in the history of the game. That alone could keep him on top as the all time greatest coach in KU history, no matter what Bill does in the future.

And somehow I don't think Bill would really mind that the mountain may just be nigh unscalable with Phog in his way.

Great points, and I wish I had time to expound more on the case for both coaches. Clearly no one can transcend Phog as the father of college coaching, whose impact on the program, its history, and the game of basketball writ large clearly was epic. (Spawner of Rupp and Smith, architect of the NCAA tournament, the force behind basketball joining the Olympics, etc.) He was, in short, a "transformational" figure at KU and in the sport as a whole. (Hence his being featured as the second portrait, right next to Naismith, at the National Basketball HoF in Springfield) Is Self a transformational figure--looking just at KU? Not yet, IMO, even though he's been HUGE for the program (not just on the court, but his role in the Booth Hall HoF, sprucing up AFH, injecting the proud history front and center back into the program, etc.). But as a pure coach on the court, Self is certainly making a run at the good Doctor. (Although comparing past and present eras is insanely difficult, of course, and really unprovable either way--for the same reason the pundits today shouldn't, IMO, say that Jordan was the GOAT...over, say, Wilt. Two very different eras, two VERY different players, two VERY different skills sets, but both truly transcendent players that are in another dimension)

Speaking of Wilt, by way of segue back to the question at hand, even if the metric were just pure coaching (and winning coaching), the big "if" of history is what if Phog had not been forced into retirement due to age and had been allowed to actually coach his most-prized recruit, Wilt Chamberlain, instead of Dick Harp? Harp was a decent coach, but he couldn't hold Phog's clipboard...and yet Harp took the Wilt-led KU team all the way to the '57 NC game against UNC. Here's the salient rub: Does anyone think that Phog wouldn't have been able to match Harp's feat of getting that KU team to the NC game? And does anyone think that a Phog-led Wilt team would've lost that game?

So if Phog HAD coached that team and garnered another NC crown (giving him two, plus the two Helms crowns), I think that the debate over who might be the better coach would tilt more toward Phog...until and unless Sir Self brings home another lovely trophy or two for our Booth Hall display case.

Just a quick-hit response. Great (and fun) question you posed...

Rock Chalk...