Robots are the better option - we send a lot more robots to space than we do humans. But there's nothing wrong with also having some human missions.
The big reason for that is that the robots are very modest in their overall capabilities. With humans, you can't get cheaper than the cost of sending one, or better few, people, but when you cross that line, you suddenly have a lot of functionality for free.
A human living on Mars could operate multiple geographic exploration rovers at much higher speeds than currently (existing rovers get 0.1mph max). This is the benefit of having a 60ms ping time instead of 6-20 minutes. Plus the ability to troubleshoot, clean off solar panels, run slightly different analyses without needing to build it into the probe 8 years ago, assemble sensor stations, etc.
Yes the mass budgets for manned missions are titanic. But with even half-way good mission planning we can get more science done than the equivalent mass of robots - at least for Mars and the Moon. Food and life support mass for long trips to the outer planets (or shielding for Mercury) mean robots will win there.
Every year tax payers specify where their tax money goes. 50% of their taxes will go directly where they decreed it be. The other 50% and any debt can be allocated by the congress.
There should also be options of "Let congress handle it" and "whatever the previous years makeup was" and options to adjust from there.
NASA will probably be better funded, by a huge margin.
This is why we elect representatives. It’s not a perfect system but the average citizen would not have the context necessary to make direct decisions on it.