I doubt 0.003" of wear is causing any problems. You have an adjustable air+fuel supply [ the mixture screws ] to compensate for variations. That is why it is adjustable.
I tuned my first carb in 1964 & I am still learning.....
I never use a vac gauge for idle adjustment, I tune by ear & feel. You want the highest idle rpm combined with smoothest running. Squirting propellant around any gaps WILL increase idle speed, that is normal.
Getting back to shaft clearance & air leaking past it. There are numerous sources for the air entering the engine at idle:
- PCV valve
- gap around t/blades
- air past idle mixture screws
- the t/slot; air from above the t/slot, around t/blade, exiting on the manifold side.
- leakage past the t/shaft.
So leakage past the shaft is only a small proportion of the total amount of air entering the engine at idle.
I have not found the hand-over-the-carb test very useful & I do not use it.