BLU isn't even a real job. It's a Limited Job. It's not a good example of anything other than a job intended to be outside the norm.
And good job moving the goal post. Nothing here was brought up about weapon damage, just your job abilities in sync content. Higher level job abilities generally comes with higher potency, which translates to more damage. So, by default, if you kept these job abilities in content not intended for them to exist you'll be doing more than the intended damage. But wait, what if your potencies were reduced to compensate for this?
You will also have more job abilities than intended, allowing you more actions than intended. Using the worst offender, Sastasha with an at level player will be outshined by a lv80 player, even if said 80 was nerfed heavily to compensate. But, nerf them harder, I hear. In which case you're putting in a tremendous amount of effort to reach the average LV15 players state of play that not even on release max level Extreme trials demand. Very quickly people will question the purpose of being so heavily nerfed when the game is supposed to be a welcoming experience.
I really hate to say that I honestly agree with the "just don't do it then" sentiment as much as I think it's a poor answer to this discussion. As much as people would enjoy keeping their kit throughout the game, the fact of the matter is you do not in situations you agree to. You agree to a sync in a dungeon before you go in, you agree to a sync in a FATE before you participate in it, you agree to a sync for single-player duties if you happen to be overleveled when you attempt it. At no point are you forced to do any of this, even Main Scenario, if you really don't want to. And, at least outside of Main Scenario, you aren't missing anything for not doing it. You are granted incentive for sure, but let's not pretend we aren't privy to intention sync attempts to provide.
If you must do a low level dungeon, and you aren't agreeing to the rules of a roulette, you always do have the option to undersize it solo or with others looking to do the same. In the case of you going into a roulette and all involved are not new to the instance hardly means they aren't using it for the other incentives provided (such as boosted experience) and could still be at-level with the content. In the event all present are max level, you're just here for the tomes - we all know this and you knew what you signed up for. That's the nature of the deal.