I remember in the past making a $6,000 bank transfers by going to the convenience store ATM taking out money and going to the bank ATM. I don't know anywhere else in the world where I would feel safe doing that.
There is also a lot of electronic money usage. Many people carry hundreds of dollars on their rail cards.
Credit cards are considered risky in Japan. My understanding is that chargebacks are not enshrined in law so its not guaranteed and whether it is or not most people presume they will have to pay if their credit card is fraudulently charged.
Convenience store payments are also popular because they are low risk and convenient.
I'd prefer to see Square be able to work with Suica, Pasmo, and all the other common ways that people actually pay for things here in Japan (besides cash of course)