Of course, you do check the oil level in your tires, sort of. Sidewall or tread block cracks are caused by the oils outgassing from the tire. Courtesy of heat, ozone, etc. Same reason you get dry skin, lack of moisture in the chemical compounds forming it.
Back to the shifting issue. I've got a few scrap shifter drums at work. If I'm reading them right, 2-3 tends to have a longer throw than the other gears. Seems to also have the most "slop" in the machining. Even on the high dollar bikes.
I use 20W50 dino juice because the motor runs cooler, the clutch feels tighter, and the bike shifts more readily. I'd assume because 20W50 fills the "slop" in the shifter drum better than 10W40 does. I made the mistake of putting 10W40 full synthetic in the Intruder the last oil change. (Normally run blend, thought the bottle color had changed, oops) Bike is unhappy, wife is unhappy, I'm mad. Lifter ticking, missing shifts, running hot...worked beautifully before the last oil change. ???
Close as I can give to a "learned or reasoned" opinion.
-WD