I would expect cash to be accepted at all hotels in Japan around the quality of a Hilton / DT. Perhaps unique to Japan, even hotels that are not staffed 24/7 may have a machine that accepts cash.

Not sure about North America, but I would expect most Hiltons around the world to accept cash. I have paid at least some of the bill in cash in many Hiltons in many countries, when not on prepaid rates (and a few times on prepaid rates which they neglected to charge in advance).

I know several Hiltons in the UK and Australia don't accept cash, but they tell you in advance. Even Hilton Stockholm accepted cash when I was there (before covid).

There is no problem using a debit card to pay a fixed / known amount, as long as it isn't the card on file and isn't used for pre-auths.