I don’t see it. If they wanted to establish a marker for ‘crossfire hurricane’ they would use Jumpin’ Jack Flash for the rallies, not Can’t Always Get What You Want. Just using the Stones wouldn’t seem like a close enough connection.
They wanted to fix the election for Hillary to win and frame Trump.
“You can’t always get what you want”
Is a way better troll than “jumping jack flash”. Even if that’s where tje lyrics crossfire hurricane came from
We wanted him, and we got him. It's not like we wanted something else, and he was the "you get what you need" alternative.
What I got form this is that I was probably putting too much thought into it and normal people just think of it as a catchy classic rock tune, without obsessing over the lyrics.