What is there to prevent me from setting up my own bitcoin exchange, slowing fiat and/or bitcoin withdrawals to a crawl, and then profiting off the arbitrage once prices start to diverge from other exchanges?
Only technical and marketing ability (and possibly legal repercussions depending on where you are located).
If you happen to be in the U.S., one of the biggest hurdles you are likely to encounter will be finding a bank that is willing to work with you (somewhere to receive and store the fiat that is sent to your exchange).
If you can figure out how to get an exchange up and running (and can avoid any legal repercussions), there is currently nothing preventing the ideas you present.