: Why didn't they move the Palantir then?

The situation is not without precedent. They lost the master stone of Osgilliath in the waters of the Anduin in a frutiless and costly civil war. The existence of these artifacts was known only to a few, and as such the Palantir itself would not be usable as a rallying point for a suicide attack.
In addition - see my earlier point on the possible course of the war. Once the city is encircled, how do they get it out without risk? they can't, once the city falls, the palantir may be removed to Barad Dur where Saurons arts can realign it to his uses...
Dave