There was no reason why The Miz was chosen to deliver Sheamus' challenge to Jeff Hardy.
If WWE wanted to work in a quick Hardy vs. Miz match, then fine, but this felt clumsy. Worse, Sheamus literally appeared on screen towards the end of the bout anyway, meaning he could easily have fired out the 'Bar Fight' challenge himself.
This idea that all heels are in cahoots is a trope that happens too frequently in pro wrestling generally. It's a simple presentation, sure, but it's hardly like Miz and John Morrison have been buddying up to Sheamus in recent months. That left their involvement a little cold.
Again, nothing was stopping Sheamus from setting up the 'Bar Fight' after Jeff had dispatched Miz. That layout would've made more sense. Instead, one heel spoke on behalf of another and then Sheamus was shown in his stereotypical "home bar".