Pete - The house, through appropriations, is doing what they are supposed to be doing as far as I know, they just do it badly. The problem is representative democracy means that if 20% of people in a congressional district want something, they have enough voting power to make the other 80% pay for their favorite. Rinse and repeat. Then there's the fact that to pass a budget, you can ignore what slightly less than half the country wants.
Seriati - I set it up the way I did because it eliminates the free rider effect of someone choosing not to fund anything via voluntary contributions. I don't see this deliberately leading to any more inefficiency than the current system. Lots of the money spent on campaigns would likely shift to SuperPAC type entities lobbying the people directly.
Pete - Corporate taxes, I have to admit I didn't consider, nor any number of other tax collections such as fuel taxes, import duties, etc. I've generally favored tax code changes that eliminate corporate income tax - but I don't want to derail. Perhaps for the sake of argument, corporate taxes get allocated proportionally based on how individuals allocated their own.
Bear in mind, I'm not really considering this in any way to be a viable political plan for a variety of reasons.
There is clearly a problem with people perhaps not understanding the full function of each department, such as commerce or labor. This could either be good or bad, with people believing whatever the 60 second spot or internet meme told them, or with people learning more about what their government is doing.