Partly cuz it works even better in bowls . . .
Are you sure? I have not tried it myself and I know it's in the 1965 patent, but my guess is that it will force you to lean the top even more, making it harder. But a bowl should help with the counter-spin/precession regens. I'm away from most of my tops this weekend, so I cannot check it.
Warning: This is way too long a reply, but it's complicated stuff -- at least to me. It'll all make more sense when you see the video (coming soon).
Maybe I should clarify "works better". Let's generalize to "rolling regeneration" (RR), wherein you boost spin rate by somehow manipulating the arena, flat or otherwise, to force the tip to roll while the top is free (i.e., not held in your hand, as it would be with a wizzzer). We'll come back to how you move the arena to make that happen.
In the RR in a
circular bowl I've tested, you give the top a good vertical twirl on the bottom of the bowl and then coax it into orbiting the vertical through the bowl's center without trying to lean it over at all. Looking down from above, the orbital direction will be opposite that of spin, as the rolling contact will be outside the top's spin axis. (You clearly anticipated this dynamic, as it corresponds to the "counter-spin/precession" you mentioned.)
You get into a state of pure rolling almost immediately with this method. When you pump the bowl for constant orbital speed, the tip rolls along a circle of fixed radius inside the bowl. Otherwise, it rolls along a slowly opening or closing spiral with little radial velocity. (Think fast car on a banked circular track.)
If you gave the top enough angular momentum at the outset, gyroscopic action will keep it more or less vertical the whole time. This gyroscopic "stiffening" of the top's orientation means that when centrifugal force (CF) pushes the top's CM outward, it also presses the tip onto the bowl's inner surface, thus increasing the normal reaction force on the tip at the point of contact.
Since friction and rolling resistance both grow with normal force, the CF effectively boosts traction -- which boosts the maximum regenerating torque achievable by pumping the bowl -- which boosts the spin acceleration rate (if you pump correctly) -- which boosts both orbital radius and speed (since we're now rolling without slipping on a banked track) -- which boosts the CF and normal force even more.
This neat positive feedback loop is broken only (a) when the user backs off on pumping the bowl, or (b) when the tip climbs over the rim. In the latter case, the top flies off, still spinning upright, and the bowl's become a top launcher! And a pretty powerful one, too. (To control launch direction, you just spill the bowl before the top escapes on its own.)
Hence, RR "works better" in a bowl than on a flat arena in that it's
much more effective at accelerating spin rate and also capable of achieving
much higher spin rates. And the bowl's at least as much fun.
But now I'm thinking that I shouldn't have called RR in a bowl "rock n' roll regeneration". Yes, in RR on a
flat arena, you move the arena with a rocking or combined rocking+circular motion with a definite
vertical component either way. But RR in a bowl works only when you move the bowl
horizontally in a circular or back-and-forth motion with
no vertical component.
So if "rocking" necessarily implies vertical motion, we should either reserve "rock n' roll regeneration" for flat arenas or just use "rolling regeneration" to cover flat arenas and bowls alike. I plan to do the latter from now on.