@AzureFlare
The math at a glance looks right. I can't see anything wrong immediately but will point it out as I go.
@CU vs Asylum
Asylum is much easier to work with because you can just fire and forget it. As long as you have a general idea where your tank and maybe a few (if not all) your party is going to be, you can make excellent use of it.
CU is a bit harder to use because not only does the AST have to channel it, you would want to try to make use of it's 10% mitigation as well. This generally leads to AST wanting to save CU for hard AoE hits if possible (Cascade) and thus you may be using it less often than Asylum, thus leading to Asylum potentially healing more.
Also technically Asylum heals more than CU if you don't get at least one additional tick on CU (800 Asylum vs 750 CU) which also lead to a positive net gain on Asylum.
@Noct AST vs SCH
I feel AzureFlare hit the nail home with the theorycraft so I'll just add my two more cents to this. While SCH is constrained by Aetherflow stacks, they also get a ridiculous amount of MP-free healing via Fairy / Lustrate / Indomitability. Fairy accounts for 2,000 potency of healing every minute that the SCH can direct to any single target they like every 3 seconds. That's MP a Noct AST has to consume to keep up with that kind of healing, let alone the 1,800 potentially free potency via Lustrate and then the 1K+ MP SCHs get back every minute.
SCH might be restricted to cooldowns and stacks but AST has to consume a lot of MP to stay in the game. Without any sort of HoT ability, Noct AST has to make up with those highly MP efficient spells via brute force Benefic / Benefic IIs. And since Noct ACT has the lowest MP efficiency of all four healer kits it'll run out of steam the fastest too. In a long fight, I can't see a Noct AST maintaining their steam while a SCH just kinda whistles happily while doing their thing.
And I just want to touch on one more point regarding context - everything has a timer and every tool in any healers kit is subject to the dance of the fight. Even though CU does more healing that Whispering Dawn, as AzureFlare pointed out earlier Whispering Dawn can be activated every 60 seconds versus CU's 90. If using WD / CU on cooldown, this pushes WD ahead because you get 3 WDs (1,969 potency) versus 2 CUs (1,500 if nothing channeled past the first tick) every three minutes.
Now, let's take that into a fight like A3S. You'll want to save CU for every other Cascade in the final phase to make the most use out of it. This means you'll be having two Whispering Dawns for every use of CU, thus pushing WD even further ahead every two minutes (1,312 potency WD vs 750 potency CUs if not channeled fully). This is similar to how AST can have every Cascade Disable'd but SCH can only Supervirus every second Cascade.