Engineers speak about the ‘Q’ of an oscillator; and the higher, the better. In the case of a mechanical watch, the oscillator is the balance wheel/spring combination. A good way of thinking about 'Q' is that it is the resistance of the oscillator to resonate other than at its tuned frequency when disturbed by something; from excitation from an outside force or beat by beat changes in friction at the pallet - anything.Zenith remains, but other former 36,000 vph disciples include AS, Citizen, ETA, Favre-Leuba, Girard-Perregaux, Mido, Movado, Ulysse Nardin, Zenith, and Zodiac
In the case of balance wheel/spring, Q is proportional to the balance inertia and to the frequency of oscillation cubed! Thus Q rises very, VERY rapidly with increasing beat rate.
OK, so what does this have to do with watch accuracy? Well, it's less to do with tests in static positions and more to do with real use. A watch is subject to movement and shocks, all of which contain a wealth of frequencies. These outside frequencies are trying to excite the balance/spring oscillator. The higher the frequency of the oscillator, the less likely it is that an outside force’s frequency will fall within the resonant range of the oscillator and disturb its natural oscillation.
The motions of your hand, impacts to the watch, etc. are generally low frequency perturbations. An oscillator with a high Q and a high natural frequency will be less affected by these perturbations than an oscillator with the same Q but a lower frequency because the perturbations will be closer to its natural frequency. Thus a higher frequency watch should perform more accurately in real use.
"Studies have established that the rotational physical activity of our wrists is concentrated at frequencies below 3 Hz and the bulk well below 2 Hz. However, the total spectrum does extend into higher frequencies with rapidly falling amplitude."
Hence, a watch balance wheel operating at 2.5 Hz (18,000 vph) will be subjected to some amount of disturbance from the motions of our wrists. A modern movement operating at 4 Hz (28,800 vph) will be far less sensitive to the concentration of low-frequency components delivered by the wrist and the tiny residual components at or near 4 Hz. 5 Hz (36,000 vph) movements should do even better.
Another critical factor in the increased accuracy of high beat escapements has to do with the isochronism improvement they enjoy.
"Favre Leube, Girard Perregaux, Zodiac and Zenith (at least) did some extensive experiments with high beat (36,000 vph) watches back in the late 60s/early 70s and concluded that high beat balances experience a decreased drop in amplitude both between vertical and horizontal positions and over 24 hours. This means that a high beat watch is more likely to have more consistent rate between the vertical and horizontal positions and over 24 hours they suffer less amplitude drop over 24 hours making them more isochronous as well."
There are lubrication issues that are more or less specific to high-beat watches as well. I believe it is widely accepted that a PTFE based fixative such as Epilame must be used on the pallet stones and/or escape wheel teeth simply to keep the lubrication from being thrown off. Zenith stands alone today (as far as I know) as the only manufacturer producing a 36,000 vph movement with conventional technology and religious adherence to their maintenance schedule is advised to avoid premature wear. Although a fast beat movement may not need more frequent servicing than a slower beat movement, it will be less tolerant of lubrication failure (due to ageing, dissipation, etc.) Apart from Zenith, interest in 36,ooo vph died out in the mid 70s.
To me it is clear that the advent of either silcon/ruby or Diapal systems could be beneficial to unlocking the widespread use of high beat movements. Of course the ultimate choice would probably be to devise a co-axial version with its 'low rubbing' geometry.