Using preprimed wood/metal can be time saving initially. The long term savings are much more debateable. There will be grease/dirt/etc. on the primer. Much of that will be difficult to see and only cause a problem after painting. Fisheye/bubbles/etc will show up.

Outside doors that are preprimered are not usually done with a good enough primer to last more than a couple years.

I have used preprimered trim when a customer provided it, but insisted on cleaning it all with thinner/alcohol(depending on the finish being used) to avoid or at least reduce theb possible problems.

That meant there was little time saved.