Great discussion, albeit with some speculation.
To answer the OP's question, for a current certification basis airplane. demonstrating compliance with the requirement for crosswind control is required:
Sec. 23.233
Directional stability and control.
[(a) A 90 degree cross-component of wind velocity, demonstrated to be safe for taxiing, takeoff, and landing must be established and must be not less than 0.2
.
]
Thereafter, presenting that demonstration of compliance in the flight manual is required:
Sec. 23.1585
Operating procedures.
(a) For all airplanes, information concerning normal, abnormal (if applicable), and emergency procedures and other pertinent information necessary for safe operation and the achievement of the scheduled performance must be furnished, including--
(1) ..... (2) The maximum demonstrated values of crosswind for takeoff and landing, and procedures and information pertinent to operations in crosswinds;.......
And to the standard:
...These procedures must be able to be executed consistently by pilots of average skill in atmospheric conditions reasonably expected to be encountered in service....
So it's not a secret conspiracy to "limit" what a pilot does with a plane, but the required presentation of information that the authorities consider appropriate to provide for the pilot.
It is useful to indicate to a pilot how much extra effort and precision they might have to apply to their flying as they approach, and possibly exceed that value. If they cannot manage the "demonstrated" value, perhaps some additional practice is warranted, as it is a "average skill" value - I think we might be expecting the test pilot to do even better!
Quick rules of thumb: If you cannot hold the runway centerline during the initial phase of the takeoff, perhaps abort, and rethink if you need to takeoff that runway at that time. If you cannot hold the runway centerline during final approach, completing the landing may be difficult. Maybe continue with caution, prepared to go around and look for somewhere else to land.