Currently my azure log analytics is configured to pull the logs from the console and the production application on aks cluster would directly log on the console.
Being heavy used application, would writing the logs on the console cause any issues?
Yes it is But very minimal. The result or impact vary depending on the kind of hardware you are running on and the load on the host. Unless your application does 99% Console.WriteLine() and barely anything else, the difference will be negligible.