Pretty much every hotel in Japan has a laundry machine, although I don't know of any suites that include one, unless you're going for a managed apartment.
The Holiday Inn Shin Osaka has a washing machine in the suites. Not sure why, but that was just my experience. You’re right that hostels and ”budget” chains like Dormy Inn will also have them.
I’ve also stayed at a resort on Sentosa Island that only had 1 self service washer/dryer machine, and I had to set a 2AM alarm clock to put our clothes in because it was busy otherwise. Usually hotels with self service laundry machines have a whole row of them. Probably by design so I’d give up and pay $10 per shirt washed.
It's mostly an effect of not having the backpack adjusted properly (using only arm straps and having those too loose.)
Which is insanely expensive compared to just going down the street to a normal coin laundromat. They are pretty much anywhere (at least in most big cities) and very quick and cheap. You can pay 500 yen at a laundromat, or 5000 yen at your hotel laundry room.
The main issue is those small dryers take an hour to do what a proper coin laundry dryer can do in 20 minutes.