@felixpetzold: I think I have the same problem.
(1) Bluetooth works
(2) I turn bluetooth off in the menu bar by clicking: 'Turn bluetooth off'
(3) Bluetooth turns off, but bluetooth icon remains turned on
(4) Cannot turn bluetooth back on
(5) I reboot my Macbook (MBA Mid-2012; MacOS 10.13 (17A405)
(6) Bluetooth icon is turned off and I can turn bluetooth on again.
I tried the hidden 'Reset bluetooth module' from the bluetooth debug menu. (shift-option click on Bluetooth icon, Debug menu). But that didn't help.
Sometimes I can turn off the Bluetooth and the icon turns off as well. Then I can turn BT back on without any issue. But most of the time I can only turn BT off and the BT menu icon stays on, resulting in situation (4): I cannot turn BT back on again.
So in my case it is not related to any device, it is the entire BT module.
Everything really feels like a software issue. Especially since this behaviour started after I upgraded to High Sierra.