Actually, the moon and the sun are two subjects that are great for mirror lenses. They don't move very fast (manual focus, live-view), they're bright, and you won't see any bad bokeh.
As for 300/4, sure, that would be nice. But it's an expensive lens, and you won't need aperture; you'll be stopping down! So 70-300/4-5.6 gets you the same thing. That said, you could mount a 1.4x TC on a 300/4.
That may be true, but not for $119.00 price, and 500-800 mm focal range. When you go in to some really large focal lengths, size and amount of heavy glass simply makes physically impossible to build classic telescopes.
This is a shot taken with the basic Meade ETX125 mirror lens which is 1900mm and f15, taken of the flimsy tracking mechanism and mounted on old and pretty heavy Benbo tripod. The moon do not fit in the frame so this is composite of two shots, at manual exposure of 1/500s, some adjustments for sharpness and noise reduction.
I'm not saying that mirror lenses are the best tool for photographing the moon.
I'm saying that the moon is one of the best subjects for a mirror lens.
Here's some stuff on mirror lenses: