Mkay, generally ornery I can accept. Narrow-minded still doesn't equate to stupid.
Spirits are the alarm, yes. They can even be the equivalent to a sentient, magical drone. It isn't at all like having the sign on the lawn without the service, though. If that spirit reports, the corporation can send a team in. If they get disrupted, the mage knows and can call the corporation to send a team in. Either way, someone is going in. You don't need to have a dedicated mage on hand to respond to that alarm, though. Mages are both rare AND expensive. It is a risk and quite possibly a waste to have a security mage on site. (And really, keep in mind how rare those are. Around 200 full, trained mages per million people, and a good chunk of those are going to have the common sense to get jobs that don't involve undue risk of bodily harm.)
So back to my point, no, you don't need the mage on hand, because that alert will go out, and there will be a response. I mean, if spirit patrols are on high value targets, why would on-site security mages not be on even higher priority locations?
As far as spirit patrols shutting down PC mages? I never said they should. The great thing about stealth is that it still works against astral perception. If they can't see you, they can't cause a ruckus. Go around them, lure them from their position, get in when they're not looking, those kinds of things are all options.