When you look at Tank & Healers, they do "play" the same as one another, Tanks generally don't have "interesting rotations" enough to vastly be different a example being DRK Vs PLD, Drk's main differences are that it has high APM (which mind you DRK's being slown down pretty heavily in DT), While PLD has more spam gcd's in general (that you get from your 1, 2, 3), Both aren't very interesting enough in variety while technically being different in reality both are very bland, the argument could be said they're "both tanks!" but that doesn't really matter with FF14 design because tanking is designed to be as bare bones as it can be, anything "unique" about being a tank has been pretty much removed from the game. Personally I think tanks should have way more rotational variety.
I don't really need to debate healers do I? I hope not.
For DPS, I actually agree with you Jobs like Monk vs Dragoon don't play the same, for the most part DPS are fine, Reaper & Summoner I dislike but I'm happy that theirs jobs for beginners (Although with summoner they need more casts per minute), "2 Minute meta" can effect this as we generally have jobs designed around bursts, I do think 2 minute meta hurts variety a bit but doesn't completely remove variety but it does sort of hinder it. I feel as if Melee are pretty "bland" as in theirs no sort of melee that deviates from the standard structure of rotation based jobs, such as having a melee with a lot of proc based gameplay ect. I'll add that I think 2 minute meta is a big reason why jobs feel the same as most jobs work towards that big burst, then cycle on a basic rotation until that big burst, hence why even if a job feels different theirs a lot of similarities to even the most "different" of jobs.
When people mention Job variety (aka jobs are samey, in the sense they don't bring anything unique on the table) I think some people want certain jobs to offer more then just rotation variety, which is another topic for another day, But I feel as the main issue comes in tank and healer design where both roles in general are suffering from having jobs mesh, all being builder spenders or in healers case just being press one button, Cooldowns/support on those jobs are pretty much the same, with small room for differences.