I agree that turntable speed control boxes, if implemented correctly, can reduce the small momentary variations in line frequency and otherwise clean up the power being fed to the turntable motor.  I employ the Basis power supply on my Basis table.  It does help, though the effect is quite subtle, and it allows for easier speed change.  But, I don't know to what extent the improvement is from frequency stabilization, and I have no idea how a meter measuring frequency variation would be useful; I have no idea of what measurement values would indicate a need for a motor controller, so it is not even of use in deciding on such a purchase.  

For the anal retentive audiophile...a mains frequency tester

You might as well include some test equipment from Fluke Instruments so as to detect the presence of harmonic distortion on the AC line. The 5th harmonic in particular can be quite pesky causing power transformers to vibrate and run hotter and overall power supplies to not operate quite as designed. If you have this then a good power conditioner can be quite helpful- if its able to eliminate the 5th harmonic. Most so-called 'high end audio' conditioners cannot (the PSAudio can and is one of the very few).

Your last sentence applies to many audiophile accessories.

I don't know what good it would do, given that there is not much you can do about the frequency and any variation would have little effect--it would really only affect a turntable with an AC synchronous motor, and even there, any variation would be so small as to be inaudible.  Save your money to buy something more useful.