Earlier quoted context omitted.
For something like a web request, all the frameworks catch the exception at the request level. Prod should not be going down. Maybe you mean requests are failing on uncaught exceptions, in which case I'd say it's working well.
For the customer there is hardly any difference that the server keeps running if a critical workflow, especially with a payment in flight, crashes and burns. Or if they are unable to work, because they keep getting a maintenance page, as the load balancer redirects them after several HTTP 500 responses.
Anyway, you prefer critical workflow like payment to show a success but actually be an unhandled error?