I was in Germany when Europe went "Borderless" You only had to show your passport wen to entered or exited Europe. Crossing borders from one country to another didn't matter.
Although when traveling in Europe even before they went borderless, driving with USAREUR plates on the car we pretty much got waved through each customs/Zoll station. I do remember intentionally stopping at the customs/border post the first time we went to France, simply because the ex- wanted her passport stamped. Going on ITT bus-trips to different countries, the tour guide would collect the passports of people that wanted the various country stamps to have them done en masse at the customs station rather than 30-60 people piling off and back onto the bus at each border crossing. I don't recall ever having to show ID to cross a border, only to check into hotels. Some wanted to hold my ex-'s passport. That *expletive deleted*it didn't fly.
I traveled all over western Europe on nothing more then my US Army ID card. (Spain, France, Belgium, Holland, England, Denmark, Sweden, East Germany, both Berlins, Switzerland, Lichtenstein, Italy, Austria.)