It's already been pointed out why letting us use our full max level kit at lower levels creates problems. But I agree that syncing down feels terrible for the most part. I think, best bet, is that there's a compromise here.
My go-to solution that I've seen shared by others before is this: All jobs should have a workable, comfortable, ideally fun and functional base kit by level 50. That means that the rotation, if the job has one, should feel like it has all of the structure in place, with further levels building upon it. It also needs movement, like a gap closer or opener, and a gauge with a way to spend that gauge. Some jobs have all this at 50, but most notably don't, and it takes until lvl 60 or 70 to even feel like the class is in a basic, playable state. I think this does a disservice to sprouts and veterans alike--it doesn't teach sprouts about their job skills early in the game well at all, and veterans don't want to sync down and be stuck with a job that has 1/4th of the buttons to press.
For some examples off the top of my head: BRD should have all songs by 50, it's very clunky not to have all three. Samurai should have Kenki and their movement buttons at 50. DRG should have its gauge and slightly longer rotation by 50. BLM should have Ley Lines. All tanks should have a gap closer by 50 and a basic burst/gauge spender. All healers should... I don't know, I don't play healers, I'm sure healers could tell you what they need to feel like they have a workable kit though. I gravitate toward certain jobs like DNC and SMN when I know there's a good chance of me ending up in lower end content, because I feel like those classes are at least mostly playable at 50, and most of my friends do the same if given the chance, because we all HATE getting stuck in one of the Crystal Tower raids with a job that feels like hot garbage to play for the next mind-numbing 15-20 minutes.
Redesigning jobs to feel like a solid base kit at 50 and then getting one new major ability button per roughly the next 10 levels would feel much, much better imo, while avoiding the issues with max level damage potentcies leaving sprouts in the dust.