It explains itself in Section 1; pretty much all the above the fold material is on exactly that topic. Trump & friends are taking the interpretation that the US presidential election is a vote on how the executive government is to be run.
As an extension of that, they're pulling power away from the unelected bureaucracy back towards the office of president - because a vote can't change the direction of the executive if parts of it are on autopilot independently of the president.
> What problem, other than judicial review, does it solve for the executive branch?
It doesn't change anything about judicial review. The thing they're targeting is parts of the executive acting independently of the president; which given the behaviour of the intelligence services is probably targeted at them but might be aimed at any of the bureaucrats.
Whether it is a good idea long term is a complex question though. This looks like an area where the separation of powers gets to murky territory. It is hard to have separation of powers given how much of it has been given to the president over the last century - the small-government strategy was a better approach than what the US has set up here.