This thing that happens every 7 years to every member of their species
No such thing in "Amok Time". Spock likens his mating drive to that of the salmon, but he never says it would be cyclic (for the salmon, it isn't - they can do it exactly once). As far as this episode goes, the mate-finding craze is a unique event in the life of a Vulcan (male?), resulting in marriage or death - possibly only to be revisited in case of divorce or widowing, perhaps not even then.
It is only in the much later "Cloud Minders" that Spock speaks of a seven-year cycle, but there he merely half-heartedly nods at Droxine's belief that "Vulcans only take a mate every seven years". He doesn't sound as if he were saying he swaps wives every seven years, so this reads more like he's saying he can choose a wife once in his life, with opportunities coming up only every seven years. After getting properly hitched, he's free of the cycle, and probably has very logical sex thrice a day and five times a night throughout the rest of his life, except when he feels like having a chocolate instead.
Starfleet would not
have to endure Vulcan maniacs at regular intervals, then. Most Vulcan males would know their mate-finding season to the day, and would arrange for a leave at that specific day well in advance - and be done with it, the drive never bothering them again. Spock's problem was that, being half-human, he didn't know when (or even if) his time would come. Also, being an outcast and a half-breed, he might have been among the very few Vulcans who would still remain single when joining Starfleet.
Note how in ST3, Spock lives through several decades of adolescence and adulthood, yet supposedly only endures one pon farr. If that one is successfully concluded with Saavik, it means an easy remaining life for Spock and Starfleet. And quite possibly for Saavik as well, because we never get told that pon farr would be an urge to copulate. It's a mate-finding urge explicitly (thanks to 1960s euphemisms), and a successful male may simply add the conquest to his one-woman harem for later use.
In any case, Vulcan males (or, on occasion, half-Klingon women thinking they are Vulcan males) go apeshit only when denied
timely pon farr. Spock, Vorik or Tuvok might all well have avoided their plak tow if circumstances didn't conspire to delay them from their meeting with the prospective wife. Again a relief for Starfleet and the respective males...
As for women, we've seen they don't need to have coinciding cycles (Saavik), they don't go apeshit even when in synch (T'Pring), and even when they do get complications, they aren't necessarily violent (T'Pol).