What if you end up spinning more than one container for that service?
How are these containers getting the different secrets they need to identify themselves? Are you attaching IAM roles to them to get secrets from some secret store?
Said it twice before: differently complex. There are plenty of potential “solutions” to the specific scenario you’re describing, but my original comment was more “generally consider X instead of Y so you don’t have to care about Z” rather than “use X in this specific way and it will simply solve every problem with Y”.
Like I said: differently complex but it’s a general solution to the problem and doesn’t require changing more “inner” things as much.