Then why play an MMO? Everyone knows thats the most time consuming kind of game. This is one of the fastest games to level in if you try.
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And that's why it won't happen. There is a thing you might be oblivious to, since you're on Balmung, but the rest of the servers get to deal with RMT and hordes of RMT bots that grind simple monotonous content to hit high levels in preparation for their various exploits. They can do it quite effectively up to about level 20-25, where mob kill experience declines sharply and killing enemies in dungeons requires more than just spamming a nuke button.
What you're describing would essentially allow RMT to boost to 60 even more effortlessly than before. This is the reason mob-chain farming isn't a thing in FFXIV (unlike XI), and it's why your idea won't happen either.
10 minutes isn't even enough for a single dungeon. (Assuming instant queues)
Such a time constrained person would be limited to one quick trial (e.g. Garuda HM, Chimera, Hydra...etc.) a day if they manage to queue instantly.
I don't think anybody would find that worth a subscription fee.