I'm not sure I buy that a multidimensional approach is easier for the GM to mentally judge in play, but I haven't run it yet so I don't know.Because there's less overall moving pieces, and those that are have a clearer balance. In 5e, you've got all the complexity of spell slots (these are possibly the most important thing to attrite if you want to avoid nova - your long thread on Save vs Suck was pretty obvious there)/piles of HP/per rest abilities/HD/consumables/more healing in 2024/etc.
My read of DH is it leans into open attrition mechanics far more like 4e did, where you can pretty easily gauge how burned down a party is based on simply Surges/Dailies. Here you've got HP+Armor+Stress as the main ones, and a lot of the Domain Card healing is pretty limited.
That said, almost universally, I don't mentally judge how much the PCs have in the tank. In fact, I don't care. That's a player responsibility. I don't adjust fights based on how fresh they are. Let the dice fall where they may.
I haven't read or watched anything that suggests I will have to change to effectively run DH. Play to find out. Sometime you find out that the dice hate you. In fact, since Players have explicit input into when and how they die, I am even less inclined to worry about their PCs' health.