The only time I’ve ever heard any kind of speed variance is when the spindle hole on the disc got punched off center, making the groove path eccentric. The tone arm will swing alternately toward the center and the outer edge as the record plays, making the speed of replay vary audibly. Showing once again that the manufacturing limitations of the disc exceed the limitations of the record player.
At one point, I had a Rega Planar 3 where you had to remove the platter to access to drive belt to move it from the 33 1/3 drive shaft to the 45 shaft. That was a PITA, and the primary advantage of an “upgrade“ speed controller was that it was push-button operation instead. These days, I wouldn’t bother buying a player with such an unnecessarily clumsy operation in the first place. Turntable power supply upgrades are just a money grab on the manufacturer’s part, as far as I can see.