Also, paying at stores, clinics, doctors, etc.. all done with PIX nowadays. Very few people are carrying cash these days. Very few clinics had a payment machine to accept debit/credit cards and now with PIX they have no incentive to do so anymore.
To transfer funds, you can specify the user's ID (which can be a phone number, national tax identification or some random string the user creates). To pay for purchases, you usually scan a QR code or copy a payment string using your bank's app/website. It's very convenient.
Absolutely, and I kinda expect this to become the case eventually across Europe, as the "cashless society" vision becomes inevitable. If you make it de-facto compulsory for citizens to operate electronically, it's only fair that there should be the sort of guarantees and accountability that only the State can provide, even if you lose a bit of innovation or efficiency.