I didn't say there can't be overlap. For example, AST having a DoT to go with Card buff play wouldn't go amiss, and AST being "the buffer" doesn't mean SCH can't keep Chain, which is the buff it has for the party (technically debuffing the boss, but tomatoe tomahto). Those overlaps can exist in some cases while still having more diversity than we have today.
Just asking so I know we're on the same page: You'd agree with me that all the healers having an identical (more or less) DPS kit is bad design, yes?
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As to the "you can do that even if WHM had access to far more": No, you couldn't. That's the point. If WHM had, say, 3 DoTs and Glare, not keeping up the 3 DoTs would make it unviable for content. If it DIDN'T, then there'd be no point in keeping the DoTs. For it to have an impact, it has to be large enough of a difference that it matters. If the difference is small enough that it doesn't matter, that likely wouldn't satisfy you, and it would make it kind of pointless. Most people don't think doing 100 extra potency every 2 minutes is significant enough a change. If Dia right now had a total potency of 311 (vs Glare's 310) instead of its 660, there'd be no real loss to never pressing Dia, and people would ask why even bother having the separate button. Say we had Aero 1, Aero 2, and Dia and they all did 311 Potency. People would complain that they're doing more work but getting no more (real) reward. For it to matter, it has to be significant enough to matter. But if it is, then it's excluding people not doing it from content.
Also, there's zero reason a Job that "does far less work" can't have "equal optimized value". The only reason not to do that is for people that want to do "more work" AND be given more for doing so. That is, not people who "are bored" or "want to be engaged". They're people who want "to do more damage". That's a different argument entirely.
There's no reason we NEED all 4 healers to have 6 button DPS rotations. None. If one has 2 and one has 4 and one has 6 and one has 8, that's not a bad thing. People can play the ones they like. SCH has long been the gigabrain healer, yet people have long played it because they enjoyed it. SB SCH was kind of hard to wring all the power out of, and wasn't markedly higher damage than its peers in a realistic sense, yet people still played it because they loved the playstyle. The gameplay - not big damage numbers - should be the reward for having a more complex kit. SCH's kit is the most versatile of all the healers. That complexity pays for itself with flexibility and utility. WHM's kit is the most simple. It has far less ability to flex into different situations, but it pays for that by being easy to perform at an adequate level with. Those are the trade-offs, not one doing markedly more damage.
EDIT: Typoes