SEE MY OTHER ANSWER, THIS ONE ONLY HELPED FOR A FEW DAYS BUT NOT PERMANENTLY
I reverted my Nexus 5 by downloading the lastest 5.1.1 Android Factory image and after 'downgrading' I let the device update OTA to receive the 6.0 update. From this point on my Wi-Fi issue is not occurring anymore.
So my workaround after I upgraded to 6.0 by the factory image and had the Wi-Fi drain issue:
Go to: Factory Images for Nexus 5 and download the latest 5.1.1 (LMY48M)
I did it through a Linux distribution (UbuntuGnome) so my steps were
slightly different from the Windows users. Follow these steps for flashing through Windows
Extract the downloaded 'hammerhead-mra58k-factory-52364034.tgz' and also extract the 'image-hammerhead-lmy48m.zip'within the extracted folder; 'hammerhead-lmy48m'
BACKUP ESSENTIAL STUFF FROM THIS POINT
Next steps will erase all settings and data on the Nexus 5
Connect your Nexus 5 to the PC/Laptop where you downloaded the files to and open a terminal or command prompt.
In Terminal:
$ adb reboot bootloader
to get your phone into the bootloader screen.
(Sometimes this doesn't work and you can still do it by using the keycombo for the Nexus 5: Turn the device off, then turn it on and immediately hold down Volume Down + Power, as the device begins booting up the Nexus 5 ("hammerhead") will go into fastboot mode.)
When the Nexus 5 is in fastboot mode type in the Terminal:
$ fastboot oem unlock
Beware, if you select yes by selecting it through the Volume+Up button and submit it by clicking the power button, ALL DATA WILL BE ERASED
after the 'oem unlock' is successful, go within the Terminal to the folder where you extracted all the necessary files for the flashing of your Nexus 5.
To flash the files:
hammerhead-lmy48m$ ./flash-all.sh
This took me about 4 minutes until completion and after that the phone rebooted into Android 5.1.1 (Lollipop), almost instantly I got the notification about updating to 6.0 (Marshmallow) and I upgraded immediately without playing or configuring the phone at all.
After all this, no drainage of Wi-Fi anymore and over a period of 7h Wi-Fi 'on' overnight, a battery usage of 26mAh (instead of the 'normal' 700+mAh)
Hopefully this also works for you!
SEE MY OTHER ANSWER, THIS ONE ONLY HELPED FOR A FEW DAYS BUT NOT PERMANENTLY