Will this 'Judicial committee' be within government or outside of it?
It'd outside of the Government*. The Members are appointed by the State Services Commission, which itself is a non-partisan body outside of Government that is responsible for employing the people who are in roles throughout the State Sector. The Government has little say in who is appointed to what role.
If its within government, then you run the same risk that you have now... it can be hijacked by a political party to advance its own agenda. If its outside government, then people may not like the fact that some extra-governmental organization is making such selections.
The fact that it is outside of the Government is deliberate so as to prevent the Government from Hijacking the system.
And if it is a republican AG, what are the chances of them approving a left-wing judge, if one happens to be selected by the committee?
Well we don't have Republicans, so.....
However, refusing a nominee based on the nominee's political views would be illegal under our employment laws, which the Government and AG would need to follow.
And who decides what a "pretty good reason" is? How is it enforced?
I haven't actually seen it happen because the Committee tends to have made sure that there are no skeletons in the closet so to speak. The closest I have seen, which was a different role, was that the PA who was selected for a cabinet minister was the wife of a senior member from an opposing party. There was a lot of trouble over whether it was within the Minister's rights to ask for her to be replaced. In the end, I believe she resigned to solve the issue.
The second issue I have heard about, again not with a Judge, was when the then PM suggested a person apply for a position and that person got it. There was a huge inquiry into if the PM had influenced the selection process.
I don't think the process you're suggesting is necessarily a bad one, just that the same problem exists with the current system... you can't prevent judicial appointments from getting political at some point, if the people in charge are more interested in politics than the law.
By separating the politics from the system then it does help to keep the State Sector closer to neutral ground. The US literally biases its state sector and judicial system with each new President that comes in. We don't have that. With the politicians pretty much removed beyond the ceremonial parts, then there is no real way to create a political agenda in the state sector.
*I should note here that when we say "Government" we tend to be talking about two different things. When you use "Government" in the US then you are talking about all branches and aspects of the Government from the Legislature to the Park Rangers. When we talk about Government, we are talking only about the people of the party that currently holds the Treasury Benches, sits on Cabinet, and has the current PM. We aren't meaning the opposition parties nor the State Sector itself. So when I say it is outside of Government, it is not within the control of the political party that holds power, but it is a part of the State Services, and thus a part of the overall government structures. It's just that the Government (Party) has very little control over the State Services other than in giving them policies to enact.