Originally Posted by
PoorInRichfield
Not that I know the answer to the OP's question, but in my case, frame geometry seems to have played a major role. On my 2014 Trek Domane 5.2, riding with no hands was really difficult and so I rarely did it. With my 2020 Trek Domane SL7, the bike is so insanely stable that I could almost do gymnastics on the bike and not fall over.
Any legitimate road bike should allow you to pee whilst moving. Stage fright not withstanding.