I don't think there's anything wrong with your perspective, but what do you think about the potential in-direct value that could come from a mission like this? Such as inspiring young people to pursue STEM, or the general population getting behind and funding other exploratory missions involving robots? You say that most NASA resources will be soaked up. That's possible, but what do you think about the potential in-direct benefits of getting the human race excited about space exploration?
This is a very very expensive way to do advertising. You will be able to do a lot more advertising to shape people's perceptions with just a small portion of the costs.
Furthermore, government space exploration is essentially a business of elites. It is only a few scientists and engineers that are involved with the space program. It is only a couple of the most elite astronauts that will get to actually fly the rockets. The vast majority of americans will have to be inspired by watching it all on tv.
This all worked out in the 60s with Apolo, but the world is changing and America is changing. Americans are watching less and less TV and are more willing to do things.
If you want to inspire people to go into STEM, it will probably be better to spend money on new and interesting educational programs to get kids interested in science and engineering. Furthermore, spending money on adult education programs would probably also help.