$125B+ (inflation adjusted) was worthwhile for inspiring people about what was possible.
Listen, I don't disagree that there were some benefits of the space program. But $125B+ is a lot of money for Velcro and inspiration. Let's keep a sense of scale here: if you assume YC invests $25k per company, $125B is 5 million startups (and 15 million or so founders). [1]
Just remember that the resources have to come from somewhere, and that if you're going to do it through government, you're spending other people's money to get things that you want. Someone else may not care about technology or the moon, and may prefer to spend that money on social programs or farm subsidies. Once you open the door that government takes the money and spends it, how can you possibly determine whose value system is better?
Also, to tie this back around to where we started, whether you support the idea of spending other people's money on projects that you like or not, my initial point was simply that risking money that isn't yours is not brave, whatever else you want to call it, because the politicians are not personally at risk of any loss. Worthless boondoggles don't even seem to negatively affect their reputation, and may even get them called bold.
[1] Note that I'm not proposing that the government should have invested in 5 million companies, but that an equivalent amount of resources was removed from the economy -- resources that could have built other things that people want.