I have not ever suggested that travelling without a passport is easy, sensible, logical etc. Just legally possible in some circumstances. So I would agree with everything you said except sentence 2. Certainly, for an EU member to travel between schengen countries it is NOT a requirement. According to the link I provided.
Quote
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.
Even if you don't need a passport for border checks within the
Schengen area , it is still always
highly recommended to take a passport or ID card with you, so you can prove your identity if needed (if stopped by police, boarding a plane, etc.). Schengen EU countries have the possibility of adopting national rules obliging you to hold or carry papers and documents when you are present on their territory.
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The difficulty is getting evidence that your passport is a ‘legal’ requirement of entry from a non schengen country into a schengen one. I have tried hard to get definitive evidence but without luck. But there is no specific ruling that I can find, but much speculation. I agree that your passport will often be checked when entering France.
Having said that. Some years ago I was the very first to disembark in Dieppe. Very large and empty dock area with little signage. A road of sorts was marked out with cones so I took a chance. Part way along, for some reason I thought I had gone wrong, so turned left between the sparsely spaced cones. Then I changed my mind again and snaked back to the original route. At that time I could glance in the mirror to see a ferry load of cars and outfits snaking with me. After about another 500 metres I came to a shed. There was a seat outside with a sleeping gendarme in it, about 50 metres before we got to him he woke with a start, jumped up and frantically waved us through. I think they have improved a bit since then.
Your first sentence though ”The U.K. passport is our evidence of citizenship for travel.” Is, of course, very correct. But that does not necessarily mean that you can’t travel without one.
John