Anecdotal, but: this is probably more of a Denmark thing and not a Schengen thing. I recently crossed French, Dutch, German, and Polish borders on 4 separate trips and had no checks.
I recently crossed a few borders too, and did not show a passport at any time. When I flew out of Germany the police did not even ask for a boarding pass despite me flying with a checked-in pistol (which is why the police got involved at all: the agent said their instructions is to call the police so they can look at it before the baggage is sent on its way). On arrival to Sweden, the "goods to declare" lane was empty and there was a little sign with a phone number and a message amounting to "call the customs people if you have something to declare".
We crossed Germany, Austria, Czech Republic, and Hungary and were checked when entering Austria and Germany. However this was just but a small inconvenience- we waited over three hours to enter Hungary from non-Schengen country on almost 40 degrees Celsius in a car. Compared to that, Schengen (still) is a godsend.
>We crossed Germany, Austria, Czech Republic, and Hungary and were checked when entering Austria and Germany. However this was just but a small inconvenience
Was that an actual check that could catch something, or was that just a useless inconvenient?
Because whenever I enter Austria, the "border check" is just a young grunt soldier from his mandatory military service slowing down cars to 30kph and waiving them through. One time that young soldier fell asleep in his booth with his hand out. Probably too much partying the night before so I can imagine his CO wasn't thrilled when he saw that.
So to me, the Schengen border checks are 99% inconvenience and security theater, and 1% actual security.
Adding to your anecdotal; went to Netherlands from NYC (passport control to get in), travelled down to Paris through Belgium. Hopped over to Italy and then to Ireland. No issues, and no id checks throughout. (did show passport in Ireland but its not part of Schengen).