Why? Everything Hubble is looking for is what we don't know or understand.
Why would a quick, put all the talk to bed photo be such a problem?
Scientists literally wait for years to get just a short time with the Hubble. The vetting process is extreme, and the things that they photograph are usually chosen long in advance. No one is going to waste that near-priceless time on putting to bed some conspiracy theory forwarded by a small group of contrary soreheads.
If Hubble took a picture of the site, including Armstrong's footprint, nitwits like you would say it's photo shopped and doesn't prove a thing. No need to waste time and money trying to convince the unconvinceable(new word?).
I doubt it would be quick and, more importantly, it wouldn't "put all the talk to bed". Anyone who thinks that the moon landing didn't happen will be able with just as much (and just as little) reasonableness to discredit photos from Hubble.
1. changing the orientation of the HST requires expenditure of thruster fuel. NASA *knows* we landed, so there is no pressing research need justifying the expense of reorientation thruster burns. Why would NASA bother to use this expensive-to-resupply material just to satisfy idiots?
2. Even if they DID reorient the HST and take the requested pics, do you really think the idiots would cease jabbering? Hell, no! They'd just start screaming about how the image was computer-generated to perpetuate the hoax.
So, basically, the idiots' calls to use the Hubble to scope the landing sites is spurious.
Factor in the fact that these sites can be scoped from the ground using privately owned reflector arrays, and have been scoped, and the trash left over from the landings HAS been spotted using such means... one is left to conclude that the idiots will NEVER shut up until they are themselves sent out of a lander onto the sites in question.
preferably: without a space suit.