When running a fleet of machines, it was always better to have them pull their config rather than push to them. It was far more reliable because you didn’t have to worry about whether a machine missed a push.
It would just grab its config whenever it came back online.
Monitoring: Mostly push, except prometheus which is pull.
Config management: Mostly pull, except ansible which is push (yes, there is ansible-pull, but most ansible code out there assumes push).
Monitoring: you don't want to have all your applications and even scripts run a thread to listen on a dedicated port to allow pulling. It's bad for security, code complexity, configuration complexity (all those ports) and reliability (when an application stops the datapoints are lost).
Config management: with a push model you can easily end up having 2 developers push to the same system (or to systems that should be updated in sequence) in an unmanaged manner.
Pull based monitoring makes it so you can remove the service and independently recognize failures.