Caused the near loss of one DC-10 and the total loss of another one, a few decades back.

That was pretty specific to the DC-10: A money-driven design decision had the cargo door open outwards to allow more cargo to fit inside. A design flaw meant that it was possible to close the door without fully locking it.

Do most airplane doors have a mechanism where “closing” is the same act as “locking”? That is, it’s impossible for the door to be closed but not locked?

Most commercial airplane doors cannot open directly outward. They unseal inward and then twist to clear outward. At altitude the internal pressure will push them directly outward and render them unable to open, even if the locks fail. In this regard they are fail-safe.

The DC-10 eschewed this standard in favour of doors that opened directly outward with catastrophic results if the locks failed.

modern aircraft doors open inwards first, this is a really important design feature.

so therefore locking becomes irrelevant. even if some crazy person goes up to the doors mid flight and tries to disarm, unlock, and open them, they simply won’t open when you’re at altitude, even though the aircraft is pressurized.

long story short the difference between closed and “locked” is actually almost irrelevant in modern airliners when the aircraft is at altitude.

Not frequent, but happened in the past. Example United 811 -- https://en.wikipedia.org/wiki/United_Airlines_Flight_811

This is what my mind immediately went to. Can't believe that plane flew for another decade and a half.