There is plenty of private money in basic science, including astronomy. The recently departed Paul Allen funded the Allen Telescope Array. The Sloan Sky Survey was funded by the Allen P. Sloan foundation. The twin Keck telescopes, one of the premier observatories around, was funded by the Keck foundation. And there are plenty of other private donors pouring money into astronomy.

Hubble could not be privately funded, as it was built as part of a joint NASA/DOD program that actually created four Hubble-class telescopes – one for NASA, and three as spy satellites. Also, it was specifically designed to be flown in the Shuttle’s cargo bay, and the shuttle was hellaciously expensive to fly. So all of that put it out of reach of private funding.

If SpaceX’s BFR flies (and it may fly before the Webb telescope is launched), it could change the entire game for orbital astronomy. Not only would it be able to launch a telescope for 1/100 the cost of the Shuttle, but its 9-meter cargo bay could carry a large telescope that uses a single mirror, instead of the folding mirrors of the James Webb telescope. This would simplify construction and lower cost dramatically. At that point, you’ll see private organizations funding space based astronomy.

One last thing – when Hubble launched, it was capable of much higher resolution than anything we had on Earth, because Earth telescopes had to view through a roiling air mass. But modern adaptive optics have almost eliminated the distortion of the atmosphere, and there are now ground-based telescopes that have significantly higher resolution than Hubble. We still need space telescopes to view objects in wavelengths filtered out by the atmosphere, but for visible light the best scopes are now on the ground. And when the new generation of giant scopes comes online, it won’t even be close.