Way to go, Beelzebubba!
That's EXACTLY what I prefer to do, spend my own money on what I want instead of the government taking it through the coercion called "taxation." "Public" money is a total misnomer and farce!
However, recognizing that the government IS going to pry my money (and yours, yours, and yours) from us some way or other, and it IS going to spend more than it takes in anyway, I'd rather it go for something worthwhile.
The Interstate Highway System is an example as were the moon trips.
Economic activity does have a multiplier effect far greater than just redistribution of wealth.
Do they shovel bushels of greenbacks into the nosecone?
We have never sent any money into space. It has been spent right here on earth, mostly in the good old USA.
Space exploration both promotes the general welfare of the US and advances our defense.
In somewhere between 100 and 200 years it will be entirely possible for ordinary people to get to both the moon and Mars without any more government help than you get when you fly an airplane from New York to Los Angeles.
It will be far better for our children if our government is the first one on Mars and the moon than say, China.