This sounds like the swedish product "swish" which is immensely popular. Nobody does bank transfers between people, everybody transfers to your mobile number. So far I think there are no fees for personal use, either, although they said it would come later a few years ago. Transfers are of course instant and you can see the recipients name before you send the money, which is a great pro compared to a bank transfer to…
Do people really transfer that much money between them on a regular basis? Everyone was touting this as the selling point for some of the crypto currencies, but I've always thought this is a non-issue. It's anecdotal but I can count on the fingers of one hand the number of times I needed to transfer money to a person and not to a company.
Right now we use Revolut for this, where possible. But that only works when the person receiving the cash also uses it, which isn't always the case. Having a more universal system that works for everyone would be very handy.
One amusing thing about doing this approach is that, if you tend to split who does the principal payment evenly between your group of friends, then you realise you are rarely adding or removing funds from your Revolut account, you are just shuffling the same small sums back and forth between yourselves in order to keep things fair.