It would be progressing if you're doing a dungeon, POTD, or HoH for the first time and getting to new floors. The key words here are 'over and over'. Once you've cleared that content, you'll need to play it again and again to level up, even though you've already experienced everything in that dungeon. If there was new and interesting content on every run (to at least a reasonable number of runs), then playing multiple times could be progression, but that's not the case.
That is true for normal RPGs as being max level with maxed gear typically means that you can easily cheese every single boss in the game, but in an MMO like this one, there's not only level sync (and item level sync), but also content meant for players at max level. The final bosses of the other Final Fantasy games aren't meant to face maxed leveled players, but rather the average leveled player for that point in the game.
However, this game provides content like Eden raids and the Yorha raids (and the current MSQ) that can ONLY be accessed at level 80, meaning you need to be at max level to experience the end game content. So if you're the type of person who doesn't want to be at max level (not saying YOU are, but for the people that are), why would you be playing an MMO that requires you to have jobs at maximum level for certain content?
I'm working on the post-Stormblood stuff right now on my main, which requires me to be level 70 or above or I cannot even access that part of the story. What if other non-MMO RPGs started keeping you from finishing them if you didn't reach the maximum level? Would you even want to play them if you couldn't finish the story without a massive grind?
If that's what you like, then do that. I admit that making alts and speeding through the first 15-20 levels with the Helm of Light is pretty fun, but you should at least have some higher goals for your main account, do you agree with at least that? (Your account has a lv 80 samurai in Shirogane btw so you clearly do)