When a critical part of a web application pod is killed by the OOM-killer or some other thing, the pod should fail. This allows the tool maintainer to see that there is a problem on that level and allows admins to troubleshoot more easily.
Importantly, it should be there in case of a scaled out application so that kubernetes doesn't keep trying to send traffic to the pod.
webservice should define pods with some minimum level of healthchecking, even if that is just making sure that it knows which process to watch. This may or may not be possible in all cases since not every app will work the same way. Simply watching TCP port 8000 might be the best we've got.