Potency for abilities is generally unchanging (unless some trait changes the ability itself and replaces it with a version with different potency or something similar), but how that potency maps into actual damage is based on gear stats. That's how the damage is 'lowered' when synching into lower level content: by lowering the stats of the gear.
Unfortunately, the level sync math is already somewhat broken, given how gear is synched down. In some cases at high-end content it can leave people undergeared to a point where they should not have been able to queue, and in many other cases at low-end content it trivializes it (hence why people can faceroll so much early content, even synched down).
Specifically, my understanding—and someone please correct me if I'm wrong here—is that a given piece of gear which exceeds the ilevel maximum will be individually synched to that ilevel by removing all materia bonuses (i.e., taking only the base stats of the gear), then scaling down by an amount based on the difference in ilevels. But because stats have gone up from expansion to expansion at a higher rate than the ilevel has, synching ilevel 500 gear to ilevel 100 will give you gear with considerably better stats than any actual ilevel 100 gear has.
And since potency -> damage/healing power is based on those stats, that "better than actual gear of this level" situation means the damage/healing output will also be higher than you could actually get at that level, contributing to the "even synched to level 50, we can faceroll Crystal Tower raids" scenario; even with abilities and traits from later levels missing, the base stats that go into those calculations are still a lot higher than they would actually be at level 50 in level 50 gear.
This is also how it can backfire at the high end; let's say someone has their level 80 ilevel 430 weathered gear and wants to queue into a level 80 dungeon that takes ilevel 435 minimum and syncs to ilevel 445. They go and get two ilevel 480 accessories, because the accessories are the cheapest and it will raise their gearset average to around i439; that's enough to make the ilevel check, since that's done as an average. But once they get into the dungeon, those i430 pieces are left untouched but the i480 accessories are synched down to i445. And since this is level synching within an expansion, the scaling down is actually fairly likely to end up being roughly equivalent to real i445 gear. Now they may be insufficiently geared to survive the dungeon effectively; their effective average ilevel is now about i432, which would not have let them queue into the dungeon in the first place.
The upshot of which is "scaling consistently without having to have synched-down stats manually set for each piece of gear—or manually mapping it to some equivalent gearset at the target level—is hard, which contributes to existing balance issues."
Much as it pains me when I see my hotbars turn to a sea of disabled icons when Roulette dumps me in Sastasha, I suspect that letting me keep level 80 abilities in there would exacerbate an already-unbalanced level synching situation. For it to work, level synching would probably need to be rethought first.