Garick wrote: It's not like the guitar that almost everybody who plays music at least tries to learn.
As popular as gitfiddles are I think that's an erroneous assumption,sir.
Back to the issue at hand.
Excluding having very small hands or a physical problem I just don't get people having trouble holding onto any of the smaller whistles,at least down to Bb. When I was younger and had no wheels I often walked for miles.Where I live it's hilly,and even a slow pace for me is quicker than most others' normal pace.So in warm seasons my hands sweated.A lot. Outside of the rare oops which was due to the walking I've never experienced this ongoing stability problem. Plus I used to prefer the nickel finishes,although like all finishes they would eventually wear off.
For beginners it may just be getting used to the pressure and balance required with both lips and digits,especially the thumbs, to keep things stable.That,not unlike using a pen,is just a matter of familiarity which becomes unconscious.
Oh,don't get the wrong idea.I don't use my lips to help hold a pen!