I just wanted to poke at this little blurb here for a moment because I feel it doesn't fully depict what's going on just yet and would like to discuss what I feel is inaccurate with this assessment.
WHMs have a total of 25 skills. If you consolidate Aero I, Stone I, Stone II, and Stone III, you're left with 21 skills. Utility of Fluid Aura and Repose aside, they still count as skills towards the kit and should remain. If you do choose to remove it, you should also remove other "useless" abilities from other kits like Spear from the AST count and the limited application of things like Spire, Ewer, and Silent Dusk.
So in essence WHM still has 21 skills. The +10 Cross Roles don't really need to be added into the final counts since all three healers get the same pool to choose from.
If you include Aetherpact and Fey Union, SCH has 28 skills. The consolidation of Bio, Ruin, and Broil would reduce it to 25 skills. Then you go onto to state 8 fairy buffs and abilities which is incorrect as each fairy only has three (Eos = Whispering Dawn, Fey Covenant, and Fey Illuminate | Selene = Silent Dusk, Fey Caress, Fey Wind). I feel the error here is that you also included Aetherpact and Fey Union when they're already counted towards the SCH skills.
In total this means SCH has 31 skills.
AST has 28 abilities. Once you consolidate Malefic, Malefic II, and Combust, you're down to 25 abilities. Add Redraw into the mix as a downgraded Minor Arcana and you're at 24. I would advise against counting the Cards towards this total number of abilities because it misconstrues how many "options" AST has at their disposal. The six main cards are functions of Draw, Redraw, Spread, Royal Road, and Sleeve Draw and the two Crown cards are part of Minor Arcana (also a function of Draw) and Sleeve Draw. Unlike pet abilities, you cannot choose what card to draw which is the important distinction. If you could choose what card you could draw, everyone would just pick Balance, thus essentially negating the rest of the pool (in theory, the only time you should be drawing a Crown card is through Sleeve Draw because you'll never want to discard Balance on Minor Arcana). Because the randomness exists, it's not accurate to depict each card count as a separate ability and implying you can use them on-demand.
If you agree with my blurb above, that means AST has 24 skills in total which isn't too far off from WHM. SCH is making out like a bandit though.
I also think it's important to include traits into this count. Even if the current Lily system is poor, it's still a part of the WHM identity and within their traits. Same can be said with Aetherdamn on SCHs. It won't change the count too much at all but I figure it's important.
So, if we ignore the shared traits (Enhanced Mind, Magick and Mend) and the spell masteries we get the following:
WHM has 12 traits. Remove 3 for Mind, 2 for Magick and Mend, and 4 for the masteries, you're left with 3 traits.
AST has 10 traits. Remove 3 for mind, 2 Magick and Mend, and 3 for the masteries, you're left with 2 traits.
SCH has 15 traits. Remove 3 for Mind, 2 for Magick and Mend, 3 for masteries, and 3 for Intelligence, you're left with 4 traits.
So in total
WHM = 21 active abilities + 3 traits = 24 total
AST = 24 active abilities + 2 traits = 26 total
SCH = 31 active abilities + 4 traits = 35 total
The skill divide is there but it's not +13 that's initially stated in this blurb and the only thing that really pushes SCH over the edge is the fact they get +6 skills via pet (arguably +4 if you consider the Summon abilities as a general skill to get to their pet).
Just some two cents to shape this particular point into a more accurate depiction.
[edit] I counted traits wrong