This was never resolved and I believe that something "deeper" is going on that warrants investigation.
With the LPCXpresso546xx board I had eventually worked around the issue by programming the on-board OpenSDA interface with the J-Link firmware which is thankfully also supported in MCUXpresso.
Now I have a FRDM-KW36 board here that I have to work with and J-Link firmware is not available. So I am back to CMSIS-DAP and back to the same "could not connect to core" issue also with this board.
I tried the ARM uVision debugger that also supports CMSIS-DAP and there, I can program the flash and debug without any apparent problems. So we can exclude any power/hardware/cabling issues or even issues with the USB drivers.
But in MCUXpresso, I was not even once successful in doing that, not even erasing the flash or anything, and this is what I'll have to use.
By the way, I got so desparate that I have reinstalled anything related to USB, used USB 2.0 setting in the BIOS, even used a plug-in (ExpressCard) USB controller card, all to no avail, all returning the same error. Of course a complete uninstall/reinstall of MCUXpresso, too, and I can't even count the number of times I have recreated a new startup configuration.
What can I do to track this down? Is there a way to turn on extra-verbose logging to see what's going on at low level?