TT, I'm not sure why you believe that a bike can't accelerate at all if the mixture is too rich or too lean.
Because fuel only burns in the cylinder when within an A/F ratio range. To me, hesitation is the lack of combustion cycles.
It is possible that it will misfire, then hit, misfire, misfire, hit, etc.
I observe this descriptor when there is too much fuel for available oxygen IE. too rich. The engine misses cycles because the extra fuel quenches any flame before it can light off, if the over rich is a borderline condition.
The engine will still accelerate just not smoothly like it should. It's not like every bike to ever have a mixture issue wouldn't accelerate past idle???
Could be a description difference, or meaning. Hesitation, wheeze, or no response to throttle advancement is what I expected the complaint was all about.
Anyway, with a slightly lean condition, it always burns what ever it has in the chamber, as there is plenty of oxygen to do so. It just doesn't burn very long during the power stroke, making poor power.
I learned this from 2 cycle engine adjusting by ear. When very rich, they will 4 cycle, 6 cycle, or even 8 cycle. Very lean and they, make poor power (and run hot) but they do fire on each cycle of the power strokes. If you go so lean as to go outside combustion range, they quit, until some more fuel is available, then resume as if nothing went wrong.
The phenomena carries to 4 cycle engines too, 8 cycling and more, as the exhaust cycles don't completely evacuate the cylinder for the new fresh charge. I call this burbling as the engine clears away excess fuel for proper and reliable combustion.
The recovery from a throttle transition can be diagnosed in this way. Clean recovery and the mix went too lean, burbling through recovery means the mixture was too rich to fire on each combustion stroke.
For combustion to occur it must fit into an air/fuel ratio range to combust at all. I describe hesitation as when the engine is firing on any combustion strokes. If it is too rich during the hesitation, the engine will burble as it gains RPM. If too lean it won't advance at all. And this is typical for mechanical slide carbs set for idle that is not rich enough when the slide is raised, raising carb throat pressure and making more oxygen available for combustion.
If the OP and you are using different meanings of the words I'm accustomed to, then just ignore my input.
Cheers,