Schengen is incredibly useful, especially if you have to transit through several countries. It's also true that the decrease in cash usage has reduced the benefit of the euro.
However, the benefits of a single currency go beyond cash. It's also about understanding prices. You see a sign for coffee and it's 1199 Hungarian Forint -- or it's 14.99 Polish złoty. It's not clear at all what those numbers mean. Sure it's possible to pull out a currency calculator app to see what the rate is today and what it means in euros. It's not an insurmountable problem, but it is bigger than a mere inconvenience. It's constant friction on not really understanding what's going on. If those coffee prices were instead 2.99 € vs 3.53 €, you would immediately see that the Polish coffee is 20% more expensive.
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As for the payment terminals offering to pay in Euro, as others have already noted, that's a scam. There is a hidden fee, usually around 3.5% - 5.0% of your total, that you get charged for this "convenience". Refusing this and paying in the listed currency will mean that your own bank will do the conversion, which is basically always going to be far cheaper.
Unfortunately this currency conversion scam is so lucrative that even big brands engage in it. Amazon for example asks what currency your card is in. If you select some currency other than what this sepecific Amazon's listed prices are in, well, you're in for another juicy hidden fee, this time to Amazon.