This is a feature request for the Logger and System Log components to add a configuration variable to define in what file/location/device logs should be written.
This would be especially useful if Home Assistant is run as a container. If all logs were written to stdout inside the container, the Docker daemon (or similar container engines) would automatically pick these up and write them to log files on the container host. No log rotation in Home Assistant would be needed as that’s handled by the container host, as well as e.g. log aggregation or persistence.