How you handle alerts really needs to reflect the volume of those that are generated.

For low volumes the success mails have value (or rather the absence of them does). When they are not received this is indicative of an incident - either the task generating it has failed, is overrunning or the alerting system has failed. The first of those should generally be addressed by the presence of a failure alert but if either of the latter two conditions apply you won't get the failure alert either.

For higher volumes this becomes impractical due to information overload but you still want to identify overrunning tasks and failures of the alerting system (and of any failed tasks hidden due to this). One option to handle this is to create a dashboard showing 3 states for all tasks - group them by priority or any other criteria appropriate and limit the actual alerts to only the critical tasks. Its a lot easier to scan down a page for any red (failed) or amber (not succeeded) than to hunt through several dozen or hundred email alerts for the few that need to be addressed immediately.