Small oddity about Windows 10: When trying to shut down the computer, it started doing a very quick reboot (without going through the entire BIOS/UEFI/bootloader sequence) back to the login screen. The event log does not help. So what gives?
Turns out, there is a setting called “Fast Startup” in the power options:

Disabling the “Turn on fast startup (recommended)” option fixes Windows’ unwillingness to shut down.
I have no explanation as for why this happens, but at least it enables me to properly shut down my machine instead of choking my power button for 5 seconds to force a power off.