He did start the first successful private space company and took over Tesla to make it the first electric car company that could compete with car manufacturing giants such as Ford. He has made other car companies start to make the change to electric by challenging them and did help America lunch the first rocket to the international space station with American astronauts and on American land. Not to mention re-kindling the publics' desire for space explorations.
NASA could do it with enough funding, but that would require the government to increase their budget, which would take years, and in the end, NASA would become political because it is taking funds away from the military, which space explorations do not need. On the other hand Teslas are inventions in my opinion because of the fact that till the model S no electric car had very good designs, was fast or could reach even half of the oil cars total miles on one full tank, but now with the new roadster coming out it will be able to drive as much as the oil car and more than gas cars. Also, you are right that a Tesla car is not 100% good for the environment, but it is much better than any other cars pollutant amount.
This is more my personal opinion, but I think the military's budget should be reduced quite a lot, and funding NASA has always been political. The introduction of profit motive into space exploration cannot be a good thing. Also, Elon Musk didn't really invent anything to do with the Teslas, and it's actually more environmentally friendly to keep your old car than it is to get a new Tesla.
I mean what furthers technology and the world other than businesses competing. Also, it is better to keep your old car, but when it eventually does breakdown it is of course better to buy an electric car. The last thing is that Elon did not invent it directly, but he certainly helped it be invented.
But also many people thought going to space would be useless and that a space exploration company could exist was thought to be impossible and wrong for businesses to enter such an industry. That is why I admire Musk he took a chance with SpaceX and Tesla even though everyone laughed at him for thinking Space X could get as good as NASA and that an electric car company could compete with giant car companies.