You shouldn't push dysfunctional branches anyways to keep the application working and always testable.

We have a CI server testing every branch for every push - I'd regard it as rather bad to have failing builds 20 times a day.

Worst case could be that it goes live because of some processes related to continuous deployment (misconfiguration happens, in companies of every size) send this to live environments and there is a chance to ruin experience for your users.