My head-canon is stating that, in this time period, the more rugged, heavy-duty grade equipment can be elected to be used when immediate threat is presumed, such as beaming over to a scientific research laboratory that's developing what could be used as a doomsday weapon being sought after by a genetically engineered superhuman tyrant bent on revenge that just attacked your ship....
I just assumed that after the austere, hi-tech TMP technology turned out to be impractical for field applications (RIP Perscan modules). Along with increased tensions with the Klingons, Starfleet reverted to rugged military equipment that culminated in the WoK Communicators and 2285 Phasers (which were just being issued). SFS equipment was, by the mid 80s, newer issue which is why the Grissom was so-equipped and a few were on the Enterprise when it shipped out for a training mission.
The assault phasers of TFF were for marines, but they were popular for the "Cowboy" starfleet captains out there and a lot of them were manufactured for ship use. With the tensions of the 90s, Starfleet accommodated, but dialed them down after tensions broke and the fleet started to slide back towards the TMP mindset of things. We even see a re-release of the 2271 phasers after some retooling because of their flexibility compared to the 85 and 87 Type 2s.