It's the golden rule, "He who has the gold, makes the rules."
The Constitution says that spending bills must arise in the House. As a practical matter, that means nothing because the bill has to go to the Senate where it can, and sometimes is, amended beyond recognition. It also means, in a theoretical sense, that the President can't introduce spending measures. That's entirely theoretical. The President has wide authority for discretionary spending and, as a practical matter, if he or she sends a bill to Congress, it gets a lot of attention. The guys who wrote the Constitution did the best they could -- and that was dang good. But, as in all human activities, politics comes in to play. And I don't think that's entirely bad.