Reading every error is a great idea, but you don't need to read them all yourself - let the computer read them for you.
This is what error aggregators (e.g. Rollbar) do. Now you've got 10-1000x leverage on your time because you're reading unique errors instead of every occurrence, and you've got more data to debug with because you've got data about the aggregates ("when did it start? what request params are common? what servers is it on?") in addition to data about the individual occurrences. You can still commit to solving them all ("Rollbar Zero"). It's just a whole lot easier.
This is what error aggregators (e.g. Rollbar) do. Now you've got 10-1000x leverage on your time because you're reading unique errors instead of every occurrence, and you've got more data to debug with because you've got data about the aggregates ("when did it start? what request params are common? what servers is it on?") in addition to data about the individual occurrences. You can still commit to solving them all ("Rollbar Zero"). It's just a whole lot easier.