In any practical environment I suppose it's common that people have scheduled maintenance of infrastructure and servers (for plenty of reasons - installing patches, reinstalling critical network appliances, etc). This affects build servers, in Teamcity's case both the webserver and build agents.
It would be desirable if such maintenance window of infrastructure, when known ahead of time, could be scheduled in Teamcity, to prevent build failures. Such build failures can cause a lot of undesirable problems and should be possible to take care of in advance of the outage.
Such build failures affects build statistics and alerts developers (via email), but that's usually a lesser problem. It might also affect unit test logic that detects intermittently failing tests. Most critically, it might affect continuous delivery (deploys), leaving any target environment in a corrupt/offline state, when the build server is abruptly removed from the infrastructure.
This isn't about accidental downtime of infrastructure, but ahead-of-time scheduiled downtime whose symptoms could have been prevented. To prevent the symptoms of which some are enumerated above, I suggest that you add a feature where an administrator can schedule a maintenance window, when all triggers will be temporary disabled, maybe even impossible to start a build job manually.
Of course there might be better suggestions, maybe even some existing work-a-round that I'm unaware of, then please enlighten me, though I don't see manually shutting down the Teamcity service as an acceptable solution to this.