Hello1,
I think your concerns could be valid, but only if the stress engineers failed to allow sufficient margin for fatigue when calculating structural limit speeds! If they got the assumptions and maths right then you could fly around for years at VFE-5kt with no problems. However, if the fatigue case was based on a specific "time of use" for flaps fully extended, and your company operating procedures are significantly exceeding that assumption, then earlier onset of fatigue damage to a flap system component could be a possibility. However, one would hope that regular maintenance inspections would pick that up and deal with it. However, if a flight procedure is significantly different from "normal", then a chat with the aircraft design organisation or manufacturer by your company engineers would probably be useful. At least then an authoritative answer to the question could be obtained.
Regarding limiting Mach No, I would suspect almost all subsonic aircraft have a sufficiently low VFE that Mach considerations would not be a concern. If they were, the flight manual would specify VFE changes with height to ensure Mach related problems did not occur.