Let me counter with this question: If you're running a random dungeon, why bother going if one of the players doesn't have X skill?
The encounters in low level dungeons are designed around having or not having certain skills. The reason it's possible to run so many low level dungeons without a tank is because it's designed under the assumption tanks don't have a number of their abilities yet.
If you made it so people kept their abilities when they level sync'd, you'd promote situations where people refuse to run dungeons with players that aren't 50 already. People already ditch groups because of a soldiery bonus, can you imagine how bad it would be if people felt it was worth eating the leave-duty penalty rather than running Toto-rak with a tank that doesn't have Shield Oath/Defiance or a BLM without Fire 3+Blizzard 3?
For example, the difference between a fully leveled Ninja and a lvl 20 Rogue is huge. Not only does the Ninja have more base skills, they have all of their ninjutsu, allowing them to, even with decreased potency, outdo a lvl 20 without those abilities in every way.
In other words, it's simply not fair to those who are leveling normally if they're overshadowed in every single way by higher level players.
The content is already easy to help train newer players how to use the abilities they have, allowing players to use their full rotations at any level would break the game in half, and require severe rebalancing of every single pre-50 dungeon, trial, and guildhest in the game. Can you imagine how trivial the guildhest teaching players how do deal with multi-pulls would be if the BLMs had access to Flare?

Level sync as it stands is there to let players be on an equal playing field when they run dungeons, at least as much as is possible. Level sync'd players already have an edge over regular players, why increase that?