That's just the tip of the iceberg. I see any one of these scenarios playing out:
1) Best case scenario: Dancing skill improves some/all of our step/samba/waltz/jig/flourish (accuracy, potency and duration) beyond their current strengths. When using Dancer as a support job, all of these potencies and durations are cut in half.
To get higher potencies/durations for Dancer Main, you'd have to convince SE that their current strengths are not sufficient and are in need of increasing at the default level before merits and gear; otherwise, see point 2.
2) Most likely scenario: Dancing skill causes some/all of our step/samba/waltz/jig/flourish potencies and durations to start out much lower than their current strengths (justifying the need for such a skill in the first place, if the difference is minimal anyway, what's the point?), requiring us to skill up and level up enough to have high enough skill caps to bring these same abilities up to their current strengths. When using Dancer as a support job, all of these potencies and durations are cut far below half of their current strengths since they already started lower to begin with.
I don't see a reason to punish the support job use of Dancer, nor the lower levels of Dancer, especially since the abilities are already balanced for what SE thinks are their proper potencies and durations AND the Dancer job was designed to be a new, desirable melee support job alternative, a function which this destroys.
3) Worst case scenario (this is SE we're talking about): Dancer skill causes all of our step/samba/waltz/jig/flourish potencies and durations to start out much lower than their current strengths, requiring us to skill up and level up enough and wear "skill increasing" gear to bring these up to their current strengths. Using Dancer as a support job becomes a joke, healing for less HP than damage taken in the time they take to use a waltz. Steps have 50% accuracy due to skill, Sambas only last 30 seconds and heal in single digits, jigs wear off before the jig animation finishes, and flourish effects fail to trigger even more often, making steps far less accurate and only really useful for their own effects since the finishing moves they provide are for the now-even-more-unreliable flourishes.
My argument (and probably many others')
is essentially: Why break something that is NOT broken? No, the support job use of Dancer is not broken; it is exactly as SE intended for the use of /dancer. No, our Job Abilities are not broken; they function like Hasso's "job ability" version of Haste (not spell or gear haste), Chakra's healing (follows a formula that is changed by vitality and gear), Focus' accuracy up (Quick step reduces targets evasion by fixed amounts), and Berserk's attack up (Box step to reduce their defense by fixed amounts), not like spells that change with "skill levels." Nothing "is weird here", as you proclaimed in the original post.
We wouldn't mind even more ways to improve Dancer ability strengths (beyond new tiers of our current abilities, split waltz timers, new merits and gear), but this idea of "Dancing skill" is NOT the way to implement it.
Do you have a Scenario 4 that I have overlooked?