Okay, I'm returning with additional info.
I've tested a lot of cables and chargers. Problem is not with chargers, problem with cables.
If you have good cable, it will charge your turned off phone with 0% battery with any charger.
If you have bad cable, it will not charge your turned off phone with 0% battery (despite being able to quick charge your phone, if it is turned on).
I don't consider this as in issue. Because I have experience with honor 8, which burned during being charged with 3rd-party cable
😁 So Asus way is better here, I prefer discharged, but not broken phone.
Good cables, work with any charger:
Asus original cable
Ikea Type A - Type C
One Plus
Baseus PD 100w 1meter
Bad cables, will not charge with any charger:
ANY Huawei
Baseus pd 100w 2meter - works only with Wotobe
Any regular Type A - Type C or Type C - Type C, e.g. for scanner or SSD.
Modern Baseus Type A- Type C cables, like 5A, 66W etc
Battery condition
Device used for testing
Tested cables:
Baseus Type A - Type C 5A
Ikea Type A - Type C
Baseus 100w PD 1 meter & 2 meter
Huawei from Huawei SuperCharge power bank
Baseus Type A - Type C 66w
One Plus Type A - Type C
Bunch of regular cables (none of them ok for my case)
Tested chargers
Asus
Baseus 45w power bank
Energizer 65w
Glo
Type C output on laptop hp 840 G5
Huawei Supercharge powerbank
Huawei fast charger with original cable
Huawei supercharger with original cable
One Plus with original cable
Tronsmart 18w QC 2.0
Wotobe
Samsung
The only charger which didn't work in that state with any state, 850ma