There are many unsubstantiated claims for cryogenic treatments of all kinds of things including improved tonal qualities in musical instruments any of which may or may not be true or subjective.  The user must use their judgement.
On the other hand, some alloy steels definitely are affected by cooling below the Mf (Martensite finish)temperature as a continuation of the quenching process from the austenitizing temperature during heat treatment since those affected alloys have an Mf below room temperature.  More Martensite is achieved by transforming metastable Austenite when cooled below the Mf.  More Martensite gives higher hardness and this would seem to be a desirable thing for brakes.
What alloy are the subject brake components made of or are you referring to the no-metallic brake components?
If it is Alloy Steel you are talking about and if it has an Mf below room temperature, then any certified heat treater will know the certified cryogenic process.
If it is the non-metallic component(s), good luck.  I cannot imagine FAA approving such a thing without a vast body of empirical data substantiating the validity of test results.

Jesus is THE life,
Leonard

Just found out from the brake OEM that the steel in the brakes is Bainitic.  Cryo only works well with Martensitic steel.  It was worth a shot!

"Cryo only works well with Martensitic steel"

This statement may have been taken out of context but does not have very much validity as stated.

A steel that is capable of responding to heat treatment so that Martensite is produced upon quenching can be intentionally or unintentionally cooled at a rate which produces Bainite.  Once in this condition it is true that cryo will not likely affect the microstucure.  However, just because you have bainite does not mean that cryo treatment would not be effective for this particular steel if you are starting from scratch or re-heat treating.

What you need to find out is what does the OEM really mean by saying the steel is Bainitic?  Do they mean that even with a fast quench you cannot produce Martensite with this particular alloy or that Bainite is the microstructure because the steel was cooled at a relatively slow rate?

Jesus is THE life,
Leonard