Two things are being confused here:

1. Except for the UK, Ireland and Denmark, EU countries issue identity cards which are valid for most situations where a passport is required, so long as nothing would be stamped: crossing borders within the EU, proving identity to the police [1].

2. Many European countries have rules requiring someone to be able to prove their identity, such as with their identity card or a passport. Those rules apply to visiting foreigners. Depending where they're from, they could comply with their national identity card, or with a passport.

So the answer is yes, except instead of a passport most people carry their credit-card sized identity card.

Since I'm British, and can't have an identity card, I'll often leave my passport in the hotel safe and carry a photocopy of the picture page. Particularly if I'm somewhere risky like a music festival or long hiking trip, where a passport could easily be lost, stolen or damaged by rain. I don't think I've ever had to show it.

[1] https://en.wikipedia.org/wiki/National_identity_cards_in_the...

At least in Germany you have a legal duty to have a passport or ID card, if a police officer asks for one but you don't have it, you'll either be brought into the next police station (if you don't have a legal address) until it clears up or show up at your nearest police station within 24 hours or up to a week, depending on the situation. Though generally if you don't have it, you usually get an oral warning and have to, as mentioned, bring a valid document of identity to a police stations (sometimes not even that). Going directly to the station is very rare in my experience.

Not having a document of identity at all is grounds for a fine of up to 3000€, though if you travel from outside the EU you'll have your travel passport anyway.

Netherland and Portugal have a similar law.

Austria has a similar law but only for non-austrian persons in Austria.

When you cross borders, even in the EU, you should be prepared that you might get controlled/checked, it usually doesn't happen but it's good to be prepared.

No, you don't if you are an EU national [0].

> If you are an EU national , you do not need to show your national ID card or passport when you are travelling from one border-free Schengen EU country to another.

[0] https://europa.eu/youreurope/citizens/travel/entry-exit/eu-c...

Yes, but an ID card is enough. Most, contrary to the US, have a passport anyway, but it is not required.

Even within most EU countries it is mandatory to have an ID card or drivers license on you if stopped by the police anyway, so the border doesn't make much of a difference.

If you move between Switzerland and Germany, you need to have a passport (or ID which was also accepted before Schengen) and will be announced when a train approaches the border. I have seen people being denied entry because they didńt have a passport.