In my company, we used to have a plugin for our bug tracker to automatically analyze .NET core dumps with WinDbg (if they were attached to a bug) and extract some useful information. We used to do this relatively often, for a shipped product, not a live service, especially if we found memory leaks.
Would you say something like that is worth to set up?
I noticed EC2 now has an API to get memory dumps. Theoretically you could automate collecting memory dumps when an unhealthy instance is pulled out of a load balancer. Then some automated analysis could happen, and allow further manual analysis.
Not sure how much it cost, but it was definitely helpful - even the fact that it was obvious which team needed to take a look first based on the objects that had leaked often made it worth it.