Traveling with a photocopy of a European ID across Europe

No, it's not acceptable.

Besides the police, what's the point?

How are you travelling? Most airplanes, some trains, checking in hotels, renting a car: they all require some form of identification. For crossing borders too, and even for Schengen borders you might need some official ID. If you lose your credit card, you might use your ID for getting money through Western Union or similar services.

Take your ID with you, and leave the passport at a safe location. If you want to reduce the chances of losing the ID use a travel belt, hidden pocket or neck pouch.

There is no EU resident/citizen database authorities could use to double-check your data and no EU-wide rule regulating this matter. As often, what the EU mandates is that other EU citizens are treated on a par with citizens. It's still up to the country to regulate police checks, registration and identification requirements as they like.

Depending on the jurisdiction, holding or carrying government sanctioned ID might or might not be mandatory and the likelihood of a check varies widely. You might also end up needing some identification document following other interaction with the police (accident, etc.) There is at least one country (the Netherlands), where not carrying ID is a (minor) criminal offense, punishable by a fine.

The downstream risks for you as an EU citizen are limited (you won't be found guilty of illegal stay, deported or banned from reentering the Schengen area or anything like that) but without any ID document, you first need to establish that you are in fact an EU citizen. I have heard of several cases of citizens being retained and put through the process leading towards a removal. Even if the mistake was ultimately cleared up, it would result in a few extremely unpleasant days/hours.

That's one of the reasons I suspect the photocopy might in fact be useful. In practice, even when the police insists that ID is mandatory (possibly illegally), if they are convinced you are an EU citizen, doing something about the lack of ID is just a burden. Lots of paperwork for something that's not a crime, won't result in a valued outcome in their performance statistics, etc. They might seize on the copy to let you go with a verbal warning. Something similar happened to members of my family (with non-official non-photo ID like credit cards).