The highest note mode works like this: if I press down C and then D, the D will sound until I release it. After releasing it C will continue to sound.

But in the last note mode, when I release a note, the synth goes silent, even if I'm still holding down a previous note. I fail to see the use of this behaviour.

That is how the last note mode is intended to work. What you are expecting is a "last note, but not really, maybe also note before"-mode. This has still to be invented.

That has nothing to do with Doepfer, but it is like that at all MIDI-CV interfaces.