Spot-on, actually. Although any job can easily just cast more sleeps since red mage is sacrificing just as much as the other jobs would because it's GCD. Anyway...
The reason the content can't "be interesting" in this sense is because you cannot guarantee a tool is in the party unless everyone in a guaranteed role has it. For dungeons, this means you can really only center mechanics around tanking, healing and the fact there are two red roles. The nature of the modern MMO beast.
Now, job design and encounter design obviously influence one another - since you can't design for jobs that don't exist. And since every job right now is a 120s burst job with slight variations in the middle, you cannot have any jobs be better or worse than any other in any encounter. I think that was actually the goal - to make sure everyone is on equal grounds of sorts (which still isn't the case anyway) but ultimately it means that encounter design is locked into a very narrow corridor since cc basically doesn't work and can't be designed around and the damage of a group is so reliant on the burst window now that desyncing it might just cause a miss of the dps check.
So everyone is forced to play the same way for "balance", battles are forced to be designed very similarly as a result, and it all contributes to a feeling of same old, same old.
Adding onto this (edit, sorry): the job you play is effectively a lens for the content you play, so if the jobs aren't fulfilling, then no matter how thrilling an encounter might be, you're still going to feel rotten about it upon entering for reclears since the novelty of the new encounter wears off. Conversely, if the jobs are fulfilling, then even mediocre battles can be rather enjoyable because, well, you're having fun just pressing the buttons.
Also, while I'm editing this post, I respect you a lot for actually trying to figure out why people are feeling this way and having actual conversations about it. Cheers <3