There are two reasons that I think skills should not be locked by level syncing. First is for fun, second is the negative-learning locking your abilities causes.

The most important part is fun. It is incredibly tedious to go into low level dungeons with only 3 abilities. Allowing higher level skills will make low level dungeons slightly easier, but the way potency and gear scaling works should keep this effect under control.

The other aspect that always gets overlooked is negative-learning that removing all your skills puts into effect. While your leveling, you tend to build bad habits based around the small subset of skills you have, and when you get level synced can cause these bad habits to resurface and makes it take a while to readjust back to having all your level 50 skills. I find this effect very strong in dungeons and a quick example would be while leveling black mage, when I first got Fire 3, I learned to use that, then did a low level roulette, got synced down and had to go back to a transpose based rotation. After the dungeon, I had break the transpose habit again. By not syncing out skills, SE would allow players to always use and practice their proper rotations.