I'm not sure what part isn't convincing you. You already have a way of spending lilies towards dps... That's any afflatus skill, aka the very mechanic of how lilies work. They just defer their DPS onto misery. 4 GCDs for 900 potency. That's 225 per GCD.
Might I add, 225 is not a random number, it's the exact amount it needs to be so that afflatus + ogcd weave = glare + ogcd clip. It's well balanced. You, objectively, shouldn't want to change that balance by introducing an afflatus dps skill.
Maybe you just don't like that it's a little convoluted and would prefer a more straightforward "lily does dps via direct dps skill". That can be a legit concern. I feel like whm is simple enough that a bit of complexity on that front (if we can call it that) isn't much of a detriment. But that's just my opinion.
SCH doesn't get any dps from it's heals, it needs many more weaving windows to get it's healing off, it's potencies are slightly lower. There are a lot of factors to keep in mind and that make this really hard to compare 1:1.
I don't really want to go into math/design essay mode but the gist of it is that what WHM is lacking are dps ogcds. Not a dps skill linked to lilies. *cough*givefluidauraitspotencyback*cough*
The argument for a dps lily skill could be made if it didn't contribute to the blood lily, but honestly, why bother.