In what sense is a time limit an "arbitrary" rule? These rules exist to balance capacity with demand. Reducing the maximum visit time increases the number of passengers who can be served, and the maximum visit time can vary between days or even different times of the same day. The alternative is to turn some passenger away entirely.
No, the alternative is to contract with other lounges in the terminal. As the BA flying schedule grows lounge usage will grow, if the lounge cannot cope with the few flights currently operating it has no chance once normal MAN-LHR schedules return.
There is a growing problem, BA needs to resolve that problem before it becomes even more frustrating for its passengers.