something more than $0.02
dementedchord,
Wrong. Normally a pinch roller pinches the tape between itself and the capstan shaft.
The pressure of that roller onto the shaft has to be within a certain tolerance. Pro machines and many better amateur machines use a solenoid to actuate the pinch roller.
The adjustment of the pinch roller travel and pressure can be quite sensitive and has to be checked every so often. But if you change the diameter of the roller you've thrown out the adjustment already. The solenoid will either bottom out before the roller has pinched the tape or the solenoid will not be able to go its full travel (where all its power is) and will be too weak to give enough force. The result is the same: weak or no pinch roller engagement: in some cases, too much roller pressure, resulting in premature capstan bearing wear/failure.
On many more amateur models, the pinch roller pressure is controlled by a spring. Even there, the diameter will affect the tension of the spring and therefore the pressure, but it wont normally be as critical a change as with the solenoid type.
To complicate matters on this particular model,
the RT-707 there were two rollers. The right hand one is a normal pinch roller and all of the above applies. The left hand one is not a pinch roller, more a scrape flutter filter and guide, so its function, and therefore its diameter, even its hardness, is not nearly so critical. On the model I have with me at present, it's not even a rubber tyre but hard plastic.
So in that sense, dementedchord is right, but only in that sense, related to this model, and its left roller.
Tape slowing down towards the end of the reel is a classic example of weak pinch roller pressure, often caused by one or two screws out of adjustment.
Tim