An interpretation of your idea is to simply have people pay for the services they need when they need them. This is how the court would work; few people would fund it until they had to do so in order to secure the court's services. But such an approach would almost certainly work unfairly against the "little man".
For example, say roads were all toll-based. If both a rich man and a poor man drive 12,000 miles per year on those roads, they would likely be charged the same under such a system. Ok, sounds fair... but now let's turn to military. What does each get charged for their protection? Do they also get charged the same in this case? Probably, but then the rich man has more to protect considering the military is helping secure his $100 million, mansion, ownership in stocks, and so on. By contrast the military is only protecting $100 and a shack for the poor man. Clearly they should be charged differently for military protection, as well as numerous other services that provide more for a rich man than a poor man... which is pretty much why we have a progressive tax system.
Even if you don't agree with that assessment, the tax system is built only to approximate the "fair share" that each person pays into it. It doesn't try to perfectly represent what each person owes the government for the services that have been provided to them. As inefficient as the income tax system feels during the winter/early-spring months, it would be MUCH more inefficient to have everyone calculate and then pay individually for their share of each and every single item in the federal budget.