tolkiens legendarium - Was the Stone of Minas Tirith still dangerous after Sauron was destroyed?

In the sad chapter of The Return of the King in which the Fellowship parts for the last time, Pippin says he wishes that they could use Palantiri to keep in touch. Aragorn dismisses this idea:

Only one now remains that you could use, for you would not wish to see what the Stone of Minas Tirith would show you. But the Stone of Orthanc the King [of Rohan, i.e., Eomer] will keep, to see what is passing in his realm, and what his servants are doing.
-The Lord of the Rings, The Return of the King, Book VI, Chapter 6: "Many Partings"

Aragorn doesn't say "I won't let you use the Stone of Minas Tirith", he says "You would not wish to see what it would show you", which sounds much more sinister - it gives me the impression that it would show Pippin something awful.

But why? We know that Sauron manipulated the Stone of Minas Tirith to show Denethor things which made him despair, and this is why Denethor became so screwy before he died; but Sauron is dead, and if he had a Stone in Barad-dûr, it should now be dormant and harmless.

Why would Pippin not wish to see what the Stone of Minas Tirith would show him? It is possible that what he saw would simply be boring and irrelevant to him (i.e., he would see Eomer looking into the Stone of Orthanc, or an empty room at Orthanc, or an empty room at Barad-Dur, none of which would be particularly interesting), but Aragorn makes it sound like something much darker was going on.

Was the Stone of Minas Tirith still dangerous to use despite the fact that Sauron was dead? If so, why?

Answer

It wouldn't be dangerous, just unpleasant. From Return of the King:

Then Denethor leaped upon the table, and standing there wreathed in fire and smoke he took up the staff of his stewardship that lay at his feet and broke it on his knee. Casting the pieces into the blaze he bowed and laid himself on the table, clasping the palantír with both hands upon his breast. And it was said that ever after, if any man looked in that Stone, unless he had a great strength of will to turn it to other purpose, he saw only two aged hands withering in flame.

^{_{Return of the King Book 5 Chapter 7: "The Pyre of Denethor"}}

I interpret Aragorn's statement as meaning that looking into the stone would be a traumatic look at a man burning alive.

For Pippin, who spent a fair bit of time with Denethor during his stay in Minas Tirith, this would likely be even more traumatic.