Do you use variable speed on your turntable?

I've had this feature on many tables but only used it to lock in the correct speed as best as possible visually using the typical complementary strobe light visual speed indicator features, not to tweak the speed otherwise.

If the records did not sound "right" when the proper speed was indicated, then there was a problem with the table and I would either have it fixed or replace it.

If you download the Service Manual of the Victor TT-101 from Vinyl Engine, you will read the following:-1 hz pitch control
The pitch, ‘A’ is standardized at 440Hz according to international standards, and is the standard for all western musical instruments. In other words, the tuning of all instruments of the orchestra is based on this pitch. But in reality, the basic tuning pitch of each orchestra differs due to the instrumentation and individual characteristics of each orchestra, as well as the personality of the conductor. The diagram shows such differences by orchestra. Most of the pitches rtange within +-6Hz of 440Hz. To reproduce these subtly different pitches, a quality turntable with highly accurate rotation is required. Another important requirement is the possibility of minute speed adjustment. If the speed of a turntable could be adjusted to the individual pitch used by an orchestra while at the same time remaining controlled by a quartz-locked servo system, the benefits of flexibility and precision would be significant from a musicological viewpoint. For this reason the TT-101 is equipped with built-in speed-control facilities which can adjust the pitch in 1Hz steps within a range of +-6Hz of 440Hz. The difference of pitches between master tape recorders and disc record cutting machines has been intentionally ignored before but now the speed of a record can be adjusted to match the original pitch of the orchestra, even if the master was recorded differently from the original performance. For example, a performance of the NHK Symphony Orchestra on one record can be adjusted to match the pitch of the same performance on a record by the London Symphony Orchestra for the enjoyment of a critical comparison.
The ‘A’ key of a piano in your home is usually tuned to 440Hz. When you practice the piano while playing back a record, you can adjust the pitch of the record to be in perfect tune with your piano.

Having tried with various 'Blues' records to play along with my blues harmonicas in various different keys.....I can attest to the fact that you can hardly ever get the pitch spot on with ANY of the records.
I now can :-)
Pretty limited use though for such high-priced complexity?

What is the point...are you serious? Records aren't cut at approximate speeds, they're cut at 33 1/3 RPM. But, what if they're not? Without a speed/pitch control you're stuck with the sound you hear. Using the control, you can vary the speed which minutely changes the sound to what was originally recorded, or what you prefer. Also as belts stretch, platters can run slightly slow so it gives you an ability to compensate for that as well. If I had a choice to have it or not, I'd have it!

P.S. Yes, I know that not all records are 33 1/3 RPM.

If I really like a particular song I will slow it down to make it last longer!