The manga cafe is one of my favorite Japanese institutions, though the utility is lower now that I'm married. It's a no-notice dirt-cheap hotel (if you're amenable to sleeping in a recliner), a mid-day nap, an instant office-with-a-door, an instant wifi connection and (typically) open outlet, serviceable liquid refreshments, climate controlled like a business rather than Japanese houses (i.e. always tolerable, which is not a hard-and-fast requirement for Japanese apartments/houses), and virtually guaranteed to be tolerant of people at the margins of society [+].
[+] This can be useful if it is 2 AM and you're in a city you don't live in with a face that says "I am at the margins of Japanese society; nobody will fault your hotel if you refuse my business on the excuse that you are fully booked... on a Thursday... but could be unbooked if I were willing to have someone from my office call to vouch for me."
Paying per minute reminds me of paying per minute for virtual servers.