Without network-manager installed, my system shuts down in 2 or 3 seconds.
Why does it take almost 15 seconds (which is a 5-time increase) with network-manager installed and can't this time be shortened?
Because it's bugged & has been for a while now
Main bug with possible self fix https://bugs.launchpad.net/ubuntu/+source/network-manager/+bug/869635
Dup bug with alternate self fix https://bugs.launchpad.net/ubuntu/+source/netbase/+bug/903825
This has worked fine here though I'd suggest you read both reports 1st
Or simply wait out a fix if one does show someday. The typical added delay is usually around 500 - 600% of your normal, so here it was 2 sec's to 12 sec's