Didn’t mean to split the log shipper for sake of security but since you brought it up :) RCE in the app allows reading secrets the application holds in memory, a lot more difficult from another process. And if you run the log scraper in a less privileged container you could restrict the blast radius to basically nothing except shipping fake logs to the central system.
But sure, take this reasoning too far and you end up with micro service spaghetti, so some balance is needed.
While in theory you can, I'm yet to see a proper defense in depth implementation despite having >10 years in the industry. In my book, if you get shell access to pod, it's game over, as these secrets in program's memory are probably also available as environmental variables, accessible in k8s Secrets etc., not to mention other ways to compromise an underlying node and the whole cluster.. But yes, this is already too far from the original topic.
But sure, take this reasoning too far and you end up with micro service spaghetti, so some balance is needed.