Isn't the whole point of saying bitcoin is not currency, but property, that you're not allowed to do this kind of accounting? I'm pretty sure if I buy and sell the same stock throughout the year, I can't simply account for it using the stock's average for the year.
Special rules apply to stocks, principally because the IRS thinks you should have really good records for your cost basis. If you had acquired them through a dividend reinvestment plan (DRIP) average market price over time is exactly what you'd use.
If you run a numerical simulation of white noise distribution of buy and sell, you'll find no profit to tax and your buy and sell prices will average close to that number.
