The best evidence of that is that the Senate does not even want a common ethics commissioner. The senators want the Senate to have its own ethics commissioner and the House of Commons to have its own. That is a good example.
Besides, there is a reason why we have this process at the present time. Should a non-elected house have any say in the appointment of the person who manages the process applicable to elected members? This separation of powers is logical. I suggest we leave it as it is.