You said both the Moon and Mars. Can you not even read your own posts?
FYI, there are not "millions of people" who would like to sit around staring at a picture that only very slowly changes. And there's no point to live video anyway because there's no action; you can just broadcast stills and interpolate between them if that's what you want. All stills that NASA captures are released publicly for people like you to oggle at.
Lastly, in case you're actually curious, there are four missions active at the moon right now: ARTEMIS P1, ARTEMIS P2, LRO, and Chang'e 5-T1. The former two don't have cameras; they're simple satellites for studying radiation and magnetic fields. Chang'e 5-T1 is just a test mission for China to advance its technology for future moon missions. LRO is the only one that takes pictures. You can see them here. Unlike Mars, a well designed spacecraft like LRO (although not a cheap spacecraft) could have enough bandwidth for streaming live HD video. But LRMO is quite reasonably designed for science, not screensavers. It has three cameras. Two are black and white cameras which are more like a telescope (as with most spacecraft cameras) - black and white for maximum resolution (every pixel measuring brightness rather than every several combined pixels). I don't know if you've ever tried to capture video through a telescope while moving relative to the object you're trying to capture, but as a general rule it doesn't work very well, and there is nothing about the hardware that's setup for video processing. The third is a wide angle colour camera... "wide angle" in that the camera images are many times wider than they are tall, designed for capturing (nonaligned) strips of the surface in seven spectral bands (which do not correspond directly to what the human eye sees, but are most useful for determining the composition of the surface)
Not that they would ever waste such an expensive instrument's time on capturing a glorified screensaver for Slashdot ACs.
If you want a screensaver satellite, find someone who's willing to pay many tens to several hundred million of dollars to make a fancy screensaver.