Most of those private expeditions were seeking short term profit (of course there exceptions like the Arctic/Antarctic expeditions but their budgets were relatively insignificant compared to the resources required to send several ships to India or the Americas in the 15th century or a spaceship to Mars. Even if colonizing and exploiting the mineral resources on Mars could be profitable in the longterm being the first on Mars (unlike being the first to sail to India) is definitely going to cost more than it's worth (in financial terms) so no rational private company would do this.