The estate may not even own the copyright to the song. Even if it did, however, almost all copyright owners place their music with ASCAP and BMI and as long as the applicable royalties are paid anyone can use the songs. The Stones don't like him using "You Can't Always Get What You Want" either, but they can't stop him from using it because he pays the royalties.
Yep. Wixen Music Publishing owns the Tom Petty Song Library, and handles the licensing and royalties. If THEY complain about Trump using it I might pay attention. Family members have no say.
You’re correct. What is not correct is the belief that a deceased artist’s song is not protected and falls into public domain to be used by anyone without compensation being paid.