If Kaaya could run, would that put extra pressure on the defense? Sure. Is Kaaya's lack of ability/desire to run the cause of our offensive struggles? I don't think so. To me, it looks like Kaaya's lack of mobility in the pocket is causing many of his issues. I think his lack of faith in the OL makes him skittish to step up into or move around in the pocket sometimes.
Earlier in the week someone posted some of the cutups of Kaaya against FSU this year and last year, and one thing that stood out to me was that on several of his poor throws or pressures, he didn't move around in the pocket to give himself a better throwing lane or a better pocket to throw from. Pocket passers have to be able to feel the pressure and step up or sideways in the pocket to avoid pressure. Dan Marino was the classic example of a guy who couldn't run but could move around in the pocket to avoid pressure. While Kaaya has a reason to be worried about his protection, I think that on several passes against FSU he didn't do his OL any favors by not sensing the pressure and moving to avoid the pressure.
If I recall correctly, Richt mentioned earlier on when he was here that he was working on Kaaya's footwork. I think that clearly is still a work in progress. Some QBs can improve their footwork and pocket presence, and some cannot. Let's hope that Kaaya can continue to get better in that department.