Exactly. Think of this search query you could do:

  source:your-app AND http_status_code:>=500

This would give you a list of all HTTP 500s of "your-app".

Or:

  user_id:12346 AND http_status_code:>=500

... to see all errors a user caused after customer care called you, reporting an error the user got. Stacktrace is there immediately without having to find the right log file on the right web server.