Both Elixir and Telemetry use error_logger only if you are using Erlang 20.x or earlier. In other situations it is not started unless there is other component that registers error_logger:add_report_handler/{1,2}.
If you are using OTP 20.x or earlier, then this process is started as part of kernel application and you cannot disable it (as this could cause you to lose information about processes that have failed).
