Schengen borders can have customs checks, but only temporarily in nature as a last resort in case of a serious threat to public policy or security, and in such a way as to impose the absolute minimum of restrictions possible.
In practice Schengen borders are comparable to state borders in the US. Sure, they technically are borders, but in practice it is just a line drawn on a map. It is not uncommon for European armies to accidentally "invade" another country because they took a wrong turn during an exercise.
They know. That’s the point.
Almost no one in Great Britain can travel to the Continent unless they are already in a boat.
I think you are greatly overestimating the size of many European countries. A significant fraction of the population lives within 75 miles of a national border. That's a bottle of water and a snack by car - if you're feeling thirsty when you leave. If you go by bike you might want to pack a lunch, but that's about it.
If you have a job, any job, you have the means to be in another country tomorrow evening.
People in the UK can travel to Northern Ireland, part of the UK, and legally walk into the Republic of Ireland, an EU member nation. So the point still stands.
Replace "abroad" with overseas then.
Only the Russian empire and the Ottoman empire required passports from foreign visitors.
That doesn't make any sense, you can literally walk to foreign countries from most of Europe. Because of Schengen large parts of the EU you don't even need any paperwork, the rationale is that it was legal for you to be on that side of the border, you strolled over onto this side, chances are you're legal here too.
If you're in a vehicle (which again, you can walk, it's not mandatory) the Schengen internal borders have no permanent checks. During COVID some of them were closed, and once in a while somebody might put up police stops - like they would for drunk driving (Americans surely have that right?) but in general in Schengen the country borders matter only slightly more than your US state borders do.