Would governments allow private space exploration?
Sure, as long as the private space concern buys all the necessary permits, taxes and license fees, files all the environmental impact studies and OSHA paperwork, and designs their craft in line with CAFE, EPA and safety standards with seat belts and air bags. Then, as long as they use a racially diverse, gender neutral, crew, they are free to go where no man/woman has gone before, subject to pending legislation.