On the other hand why don't they point the Hubble at the Sea of Tranquility and zoom in on all the trash we left up there and just end all the speculation?
Hubble doesn't have the resolution.
It is said that Hubble is based on keyhole spy satellites. If spy satellites could read a licence plate at 200 mile altitude, (unlikely) that would be a 3" resolution. The Moon is 250,000 miles, 1000 + times the distance.
3000" resolution is 250 foot resolution on the moon surface. The LEM decent module is the biggest thing left behind and is on the order of 10 feet accross.
The laser reflectors left behind by all 6 missions can be detected however and have been reflecting reliably to get distance measurements.