You are right. The fact that cashless transactions are built on a pull model, where a shop/service is charging you instead of you being the one who sends the money, is absolutely fucking insane. I recently lost a few hundred bucks just because the shop used the wrong currency to charge me, leading to a double conversion at the absolutely shittiest rates, and by the time I got to someone in charge, the transaction was already cleared and set in stone. With a sane system this never would've happened.

In my home country they actually recently started to adopt such a model. Instead of you giving the card# to everyone, they instead show a QR code with all the necessary payment details: BIC, SWIFT, IBAN, the rest of scary numbers, order number and the invoice. You just open the bank app on your phone, point it at the code, review the sum and any possible fees, press confirm, and the moment the transaction is cleared the page just reloads automatically with order confirmed. I believe there's also a special URL schema for when you don't have a PC, but I haven't tried it yet so can't tell for sure. With this approach, subscriptions are much easier to manage, because it's the bank's job to send the money, so they can list all recurring payments on a special page where you could just cancel one. Also helps with scummy services that stop providing service the moment the subscription is canceled - they won't even know you did until the the next day the payment is due.

EDIT: There is indeed a custom URL schema, and lots of cool stuff like offline payments without plastic. But some of it is still clunky, including subscriptions, which only a few banks support and most services are opting to use their own billing systems for now.