Actually Space exploration did not stop after the moon landings. Many people seem to think so but there have been a great many space exploration craft launched since them. The voyager craft are probably the best known, but there have been soft landings on Mars. and probes sent to Venus, Mercury and numerous moon in in our solar system. Earlier this year one such probe finished it 'job' by diving into Jupiters atmosphere and sending back data as long as it survived. We are getting there. Slowly but surely. But there is little left to learn on the Moon, and manned travel to the other planets is still outrageously expensive because of the amount of food the craft have to carry to feed human astronauts for the time it takes to get there and back again. A year or 2 ago there was testing of a new 'Ion-drive' space engine. It is better but still dont give us the speed we need. But at least now a one-way trip is possible. Will you volunteer for that ?
Well of course it does. A government agency does not have to do anything useful, it only needs to avoid embarrassment. A private company has to show results and make a profit. You might have noticed that manned missions tapered off drastically after people started saying "NASA - Need Another Seven Astronauts".
You may be right that "Private Enterprise" is needed, I have heard of 2-3 companies formed to do just that. I wish them luck, but sadly have not heard anything from them since their initial announcements. It aint easy ;-))