Prior to the pandemic, if you had a flight-worthy plane of any size, you were using it continuously. Once a plane was no longer being used continuously it was likely about to be permanently retired.
>Bleed air is tapped at the 5th and 9th stages of the HP compressor and from the fan.
https://hursts.org.uk/airbus-technical/html/ar01s19.html#idm...
(Airbus doc but the engines are CFM56 on the 737 models listed) Also according to this page the CFM56 doesn't have a turbine bleed air takeoff.
And bleed air is indeed always taken in the compressor, never in the turbine. First there's no point taking it later than the compressor, you just want compressed air. And it's ultimately used to ventilate the cabin, you don't want fuel vapors or smell.
All is explained in the link I posted, would recommend it as good introductory reading on the subject.