We need to see some hard equations here. It's not a debatable subject.
1 = 1, INPUT SPEED = OUTPUT SPEED, Rotational velocity both receives and sends at the same speed; conservation of energy, energy can be neither created nor destroyed without the expenditure or expulsion of force.
I've understood since I was a 5 year old kid playing 78s that idlers were speed neutral, they neither add nor subract rotational velocity. The rim would have to shrink or expand during a half-turn, with the change in mass being created from or sent to a fifth dimension. It can't happen.
The angle of the two contact points remains fixed. It can't change, it is hard-coded into the construction of the wheel. The angle of bisection would have to change during rotation for there to be a speed differential.
P.S. I have several Lencos, an idler CAN affect speed if the ANGLE between motor pulley and platter changes. If the receiving point remains at the same place on the motor pulley, but the drive point is moved INWARD on the platter, then the platters's driven radius becomes smaller and the platter turns faster. That's not the SIZE of the idler, but how the lever holding the idler is bent.
On a Lenco the idler describes an arc UNDER the platter, if the EDGE of the platter is driven then even a skewed idler does not affect speed (except via edge crawl)