I'm with you in that it's probably rare, at least if we are talking about mistakes leading to immediate catastrophic failure.
Not putting together correctly however: almost all the time from what I've seen. In the 20 or so used cars I've owned, I would say none of them were correctly put together after service. As an example; rarely seen an aero shield or a wheel liner correctly re installed. At best, they are just missing a clip, but often much worse. An authorized BMW shop that did work on my car routed a front wiring harness branch on the outside under the front bumper, completely exposed to the elements. Under carpet sound deadening and butyl water ingress liners are items that "mysteriously" disappear little by little every time work is done in the cabin or trunk areas. Small speakers are notorious for getting permanently disconnected any time work is done behind interior panels, resulting in a sound system that's not what it once was.
In fact, exactly this happened on my Model S when it got its trunk chinch actuator replaced by Tesla a couple of weeks ago. Not only did I lose the trunk speaker sound and beep at close but the whole trunk area now rattles like crazy because fastening clips were lost or broken.
While each of those faults may not be catastrophic on their own, they add up over time.
I'm not advocating for avoiding oil changes in cars that need it. Just saying that faults created during service is likely a factor in OEMs deleting service requirements.