…in systemd-nspawn: they have a proper init system as PID 1, as well as service management, so that they can actually reasonably process coredumps inside in parallel to whatever else they are supposed to be doing.
Of course, containers in the Docker sense are not like that: they typically run in some weird mixture of "i am an independent system" and "i am part of another system", and the payload is run as PID 1 without any further service management available.
Bummer!
With v257 there's now a knob to address this situation too. systemd-coredump can now be configured (opt-in!) so that it will try to process coredumps of containers *on the host*. If you set EnterNamespace=yes in coredump.conf it will acquire access to the container's mount tree, mount it within its own private mount namespace to some special location, and then run coredump processing on that – while being part of the host runtime in almost all ways.