Well, yes; and in practice this ends up meaning that those who can't afford private representation (or high-quality representation) are at a disadvantage in the system

Oh yes, absolutely. As seen many, many times in lawsuits against large corporations that simply stall their opponents into bankruptcy. And I personally believe the legal principle that you can't sue the government to be prima facie absurd: The government, of all possible bodies, should never, ever be above the law. The laws that it passes should be as binding upon itself as upon anyone else, and it must be accountable for its actions.