The vast majority of people who pay zero income tax do pay sales tax, property tax (even if in the form of rent, which always includes the owner's property tax costs), etc.
If there were a flat rate of (say) $25 minimum, what would be the cost of administering that flat rate, and what would be the rate of return to the gummint for collecting it, enforcing it, etc. Would it be worth it? You might bend over to pick up pennies, but not everyone thinks it's worth their while.
I think everyone should pay some federal income tax. We all need to be invested in America, and have some stake in how the money gets spent. If 47% pay no federal taxes, then that's 47% who don't care about federal spending, and thus we have out-of-control federal spending. If everyone had to pay something, then everyone would pay more attention to federal spending, and would vote to get it under control. Even if you only make $20k per year, you ought to pay, say, $200 federal income tax. We need something to make people a part of this country, and to care about how it's run. If half of all Americans have no stake in it, then we're doomed.