In general, the branches of the US government can be arranged by timescale of concern. The executive is concerned with immediacy, constantly. The legislature is concerned with the middle term, annually, and the judiciary is concerned with the permanent, when they percieve it as arising.

The idea with the Advocary college is to be concerned with the spurious and intermittent, and to attempt to create it.

The powers given to the Advocary College are mostly closely constrained. They can indict a President. That's a long way from convicting one. Another basic idea here is to put the gripes in the government, where their gripes will be heard. The US government is so big now, it should in a sense contain some outsiders, formally. Thus, the College is almost randomocratic.

Another way to look at it is like subtractive synthesis. In music synthesis, you can build up sounds from sine waves, which is additive synthesis, or you can filter noise until you get something interesting. The existing government is additive synthesis, but the source sinewaves are pretty sloppy. In general, something needs to be added to the mix.

On the matter of a national correspondance school, (Hi Sam!), that gives them something to do if the President doesn't warrant indictment, and it jibes well with not requiring a college degree for anything.

Having their own route to proposing Amendment will help fix any problems or glaring opportunities that arise.

And for some things, like pardons of executive branch people, just having one more branch looks pretty handy.