And who picks the members of the commission? If the prime minister and his party are the ones that select who to add to the commission, they can stack it with partisan hacks.
The State Services Commission does. Basically, if a member of the Committee is leaving then the Committee will select a new non-partisan member. While I can't say for sure, it would not surprise me that the outgoing member often has a say in their replacement.
And who decides illegality? Again, if this were the system adopted in the U.S., Barr could have rejected people for no good reason (other than they weren't right-wing enough), and when someone said "that's illegal", well, he's head of the DoJ. He sort of has significant authority there.
Our AG has limited Authority. The legality of reasons to reject a nominee is bound by the Bill of Rights, so there is no real argument to be made there if the rejection violates the BoRs. Technically the Human Rights Commissioner could lay a complaint against the AG, or the Employment Courts could be brought in to deal with any alleged illegalities. If it was considered a bad enough breach then there are certainly Parliamentary Enquires and censures as well as the Police if there is deemed to be criminality. The AG is not the head of the Police or any investigative bodies here.
The issue is not "how well does a system function when everyone is behaving", the issue is "how robust is the system when you have people trying to break it".
You may not have seen any problems with the "commission picked/AG confirmed" process. But I suspect your politicians are not as corrupt as the republicans in the U.S.
Again, I want to stress that your method of selecting judges is not a bad one. It seems fair and looks like it would get good results. I just don't believe ANY system would be safe from being corrupted, if they had someone like Moscow Mitch or Bill Barr involved.
One of the strengths of our system is that we have spent a lot of time and effort divorcing the Government benches and the State Sector. Civil Servants work for the Crown, not the Government. The Government Ministers (Basically your Government Secretaries) are not the heads of the Departments, but rather they are there to act as intermediates between the Department and Government, to help learn what the Department has need of, to formula policies to help them achieve their goals and to hold them to account for their ability to carry out the policies of the Government. The Ministers also tend to be held to account when a department fails in its goals.
There is a separation between the politician and the department itself. The Ministers guide and give policies, but it up to the head of the department, who is appointed by State Services, to implement those instructions and policies.
Essentially in our system, the likes of a Moscow Mitch of a Bill Barr would be unable to do a lot of damage because of the way the systems are set up to be reasonably independent of the Government Ministers themselves.
This is why we have cabinet shuffles so often. The ministers themselves are kind of interchangeable. Imagine trying to do that in the US where you shuffled the jobs of all the Cabinet Secretaries every 6-12 months depending on how well they were doing. (Another difference is that all our ministers are elected members of the Parliament, usually from the Government and allied benches, rather than being purely appointed by the Executive.)