I switched the device to be default sound cart. Play back from iTunes and spotify is working fine.
I just gave it a try and started recording into Garageband, and it had some issues after I tried with Cubase before.
I restarted the LR16, then it worked fine for both play back and recording, as well as monitoring.
However the issue in Cubase remains unchanged.
Could it be that, as soon as Cubase is trying to use it as ASIO source the device has some issues?
I know, on Mac that should be CoreAudio instead, but Cubase on a Mac still calls it ASIO also with my other sound carts.
So it could well be that the issue is within Cubase, but I wonder if anyone had a similar issue? Since I have two Macs with identical setup (as listed above) and I have the identical behavior, it seems it is a reproducible systematic issue…