I'm getting in on the WHM pain train. My Suggestions:

I'll start off by saying SE could be trolling us all with this and everything we've seen could already be changed, but based on what we have at our disposal, having read all the tooltips for all the healers, I have some things to say before y'all make a huge mistake.

The issue is the RNG. All the other Jobs have a lot of control over their new systems, whereas the Lily procs being a 20% chance on spells that are not even our bread and butter really pigeon holes us. If the gimmick is going to be the use of Lilies to reduce the CD's of your heal bombs and the use of Confession + Plenary Indulgence (which is begging to be spammed with a 15s recast, and no MP cost), then there should be a more reliable method of obtaining these resources. This is made a doubly poor decision by the fact that Confession stacks, which decide the worth of our new max skill, fall off after 30 seconds.

Issues:

-A 20% chance to grant confession on Cure I/II should be a supplement. Cure I/II should be the only things that grant us the 20% chance on crit to reduce the CD of Assize and Asylum (this I like don't change it). They should not be the soul source of BOTH important new resources.
-Confession does NOTHING but fall off if unused, and the chances of it being stacked in the first place are abysmal.
-Regens and Insta-Casts are a WHM's main tools - NOT basic heals - yet with the exception of Benediction's shortened CD they remain completely unchanged and offer us nothing in the new system. They're affected by it, but don't contribute to it.

Solutions:

Stacks of Confession should be permanent until used.
OR
They should grant some sort of benefit in the event they fall off (a small heal, a debuff removal/resistance, or a Lilly to the WHM), though the former seems more reasonable given the structure they seem to have set up with the kit.

I wouldn't put the persistence of the stacks of confession up for debate. They should have no timer. Period.

-Everything that uses a Lily; Assize, Tetragrammaton and Divine Benison should GUARANTEE a stack of Confession on anyone they hit. Maybe also a maximum of 1 stack granted in Asylum. You might be able to balance this by only granting Confession if a Lily is used, and grant improved returns (i.e. 1 Lily used = 1 stack of Confession, 2=2 and, 3=3)
-Plenary Indulgence should have a longer CD, and should GUARANTEE a Lily.
-Benediction should GUARANTEE a Lily.

OR

-Cure III, both Medicas, and Regens should also stack Lilies and Confession, though maybe at a reduced rate (10%, 5%, 1% respectively)
-Thin Air should have the added effect of giving you 3 Lilies instantly. We'll have access to Lucid Dreaming anyway, so we won't lose out on the benefit of 0 MP cost if we use Thin Air for Lily generation.

OR

-Dealing ANY critical hit should have a chance of granting a Lily. Any crit heal or crit damage.
-Any crit heal should stack Confession.

Reasoning:

The idea seems to have been built around reducing the CDs for your heal bombs so that you can burst out the most heals of any healer, in exchange for having only one native raid utility (sort of): Devine Benison's shield. The issue is that you have to cast (statistically speaking) 5 Cures to reliably get 4%, 10 for 10% and, 15 for 20% CD reduction to be used on ONE ability. If this is the foundation of our new setup, we need better chances than that.

The stakes are the same when depending on the generation of stacks of Confession, which have only one purpose: An instant, free group heal on a 15s CD. It seems like the Plenary Indulgence was meant to heal the party/raid, but the Tank is clearly going to see the lion's share of it's use, and using it like a professional healer sound's impossible. What I see happening is the healer spamming Plenary Indulgence every 15 seconds just in case someone somewhere has a stack of Confession that's just about to run out.

WHM's changes are different from the other Job's changes in that the WHM has EXCEEDINGLY little control over the new mechanics around which the Job will now revolve. My suggestions put the power of the new system into the hands of the player AND encourage them to put their new abilities to use strategically. Stacking Confession on the party as a contingency for a burst heal, and being rewarded for it with the keys to it's new mechanic; the Lilies could make WHM the Healz version of BLM: building and burning it's resources for a constant stream of perfect health, or burst heals that can hold a candle to the raid utility of the other healers.

FFS WHM is supposed to be the "Pure healer" but an AST in EITHER SECT has stronger basic heals.

In summation: Either give us control over the generation of our new resources, or make them MUCH more abundant.
And again: MAKE CONFESSIONS PERMANENT.