I'm not sure Petersen will start Browning if he thinks he's just going to get crushed behind a young, shitty OL. You don't want to fuck him up by getting him killed. That's when QB get trigger shy and their mechanics get fucked up. There are examples of it happening at every level of football. I think Browning will get a shot to win the job, but it's something to think about.
For all the talk about how Carroll started Barkley, at least Barkley had good talent around him. He also had to beat out Aaron Corp for the job. Corp was worse than Miles.
Andrew Luck redshirted at Stanford. He was obviously way more talented than Tavita Pritchard, but Stanford was still building and Harbaugh probably didn't want to fuck him up. A QB is different than a RB, WR, or CB.
The best players should play, but long term should come before short term, especially for a UW team that isn't doing anything next year anyways. Browning will always have average size and average (at best) arm strength. He's not leaving early. Would you rather he starts his first year for a team that will probably suck? Or as a 5th year senior for a team that will hopefully be really good?