It's a huge danger. This is why there are so many Bitcoin ATMs in convenience stores. Scammers call vulnerable people and induce them to send them Bitcoin. The number of people who you can convince to withdraw hard currency from their bank and feed it into a Bitcoin machine on the request of their "sick nephew" or "Microsoft Security Team" is mind blowing. Even elderly former police and attorneys do this.

Push payments make it much, much easier--now it's just a click away. The risk is higher for the scammer and it's easier to trace as compared to Bitcoin transfers. But it will be an endless game of whack-a-mole, and because the losses won't primarily fall on banks, payment networks, or other least code avoiders (unlike with credit cards--especially--or other forms of pull payment in general), there's less direct economic incentive to do prevention. We'll likely end up with more centralized, government policing, which will be far less effective and generate more political friction.

Push payments are the future. They're already ubiquitous in many other countries. But while it will streamline day-to-day transactions, there are going to be many more victims of fraud left holding the bag. And you can see this in Europe, where push payment fraud is rapidly expanding.

And even if, in nominal dollar amount, total push fraud ended up equivalent to pull (e.g. credit card) fraud, the social cost is greater as you end up with a small number of people bearing all the costs, whereas with pull fraud the costs are effectively spread across society in the form of slightly higher transaction costs and goods & services prices. There's no built-in transfer mechanism (i.e. tax) like that in push fraud because the incentive and accountability structure is radically different, notwithstanding that in the abstract it's a very simple change in who is considered the initiator of a payment.

The proper response is to ask for the cash price.