Paying the local currency with your own cards seems simple and works?

If “your own cards” are with non-neobanks, they tend to offer poor exchange rates, and add commission on top.

Yes, zero Forex fees cards work. But the terminal detects that your home currency is different to the local currency and you still have to choose the right option.

For example, just the other day I fat fingered the screen and chose the wrong currency.

Wise cards are still issued in your home country however. My NZ-issued Wise card still triggers the DCC prompt so it's more or less the same as a NZ-issued card from any other provider. A common misconception but understandable given how Wise markets their card products.