Yes, you're probably right, HDMI disconnection shouldn't do any bad.
I have noticed that the crash happens nearly every day around 5am.
That's interesting. To my knowledge, Kodi doesn't have a stand-by mode (as well as RPi itself), but CRON jobs will run occasionally. I just had a look at my /etc/cron.d folder. The only service I found is e2scrub_all, which checks all EXT file systems. Maybe that check runs daily, and crashes Kodi in case of errors. So you could check all your (network-) connected EXT devices for errors manually.