Technically you can also remove surecast as nothing really needs it (you just move into position), and maybe even esuna depending on what content you do. Leaving only two Lucid and Swift which are a must. Personally would forgo role actions given they aren't independent per the job and are across roles (healer, tank, ranged, melee).
As for two, I don't think two would be enough tbh, because one would probably have a niche attached to it while the other would be the standalone which wouldn't really differentiate our gameplay meaningfully unless both are niche then that wouldn't be solving anything really. I'd say a minimum of 3 is needed where niche can fill one or two but the third should definitely add something meaningful.
The one you recommended really wouldn't impact our gameplay meaningfully cause it would fall under the same issue as a dot does. Use it when available, otherwise 1-1-1-1-1.....same with the buff (use within two minute meta) [specific cases]. I think a more meaningful change, for example, would be a system that feeds into itself.. by moving whm's heal kit solely to its lily gauge and then letting glares generate lilies (not just having it generate a skill to do more damage as this unlocks options) while having an optional spender on just adding onto damage while also contributing to the lily gauge. The finality of the lily gauge, Afflatus Misery could have an ender skill on top of that (that being two). Then perhaps a follow up to holy so in dungeons you are also not spamming one button. Then having more versatile skills that answer new problems other than just healing to fill the heals that were removed for the redefined system. This giving synergy within the kit with 1 skill being game changing because now your lilies can be manually procked, the afflatus ender skill being as use-case, and the holy followup being more niche but directed to more specific scenarios (2 niche or specific use cases, 1 game changing) (You could also add synergy with the holy followup generating lilies but you get the point.) [As this only being idealistic and used to serve as an example, don't take this as what I would truly want (I just want change), this was primarily to use as an example.]
I have mentioned the issue is the entire job and not just dps skills. DPS skills would just be the start of undoing uninspired job design the next step would be incorporating them into how the job as a whole functions.