It is all a matter of scale. If something is in one's individual or corporate interest, funding will be available privately (venture capital) at that level. When something is of national interest or importance, then the capital to support it should, necessarily, be on a national (public) level.
If your private money model had been solely in effect in the 1950's, it is quite likely many tens of thousands more people would have been crippled or killed by polio. Jonas Slak was working for the Virus Research Labratory at the University of Pittsburgh School of Medicine. Albert Sabin was the Chief of the Division of Infectious Diseases at Children's Hospitial Research Foundation. Both were supported, to a great extent, by public grants and stipends.
These scientists also worked cooperatively with researchers in other countries (such as Mexico, United Kingdom, the Netherlands, and the Soviet Union) to find the cure for polio. Had these people worked independently, funded only by such monies made available by drug companies or private donations, how much longer might their discoveries been made?
You make the giant leap of faith that pictures of rocks and dirt from Mars are in the "national interest." I say that keeping more money in the hands of the people who earned is is more beneficial. After all, what is the "national interest?" Is it some sort of collectivist concept? Or is it simply the well being of the many individuals who make up the nation? If it's the latter then it's clearly better to keep the money with the people who earned it.
Salk and Sabin etc.
Good example; however, drug development and testing is one area where private funds are widely available (pharmaceutical companies and their stockholders) If Salk and Sabin had not been supported by grants then they would have been supported by private funds. Their job choice was not made by lack of research funds. Read Bastiat about the lost opportunity cost of publicly funding various enterprises.
funded only by such monies made available by drug companies or private donations, how much longer might their discoveries been made?
I suspect that had the money all been private, then the discoveries would have been made sooner. Don't forget that faculty members of publicly funded institutions are expected to teach, serve on committees, and above all kiss the a$$es of the administration in addition to the research that they do.