UPDATE: After seeing the comment regarding contamination, and researching some more, I believe I agree that my off flavor must be due to wild yeast contamination. My downfall must have been a combination of weak yeast pitched directly from packet without starter and plastic PET carboys with liquid fermlocks that probably either went dry or sucked water back in, contaminating the brew.
There's a lot of information, and people discussing multiple factors regarding this, and I don't know enough of the science to speak to that.
In my experience of 3 years and roughly 30 all-grain brews, I have never, until my last 20 gallons, failed to bottle at about 2 weeks, give or take a few days. My last batch was bottled at a little over 4 weeks, and had a flavor my friends and I now refer to as band-aid flavor, and we've come to expect this from the 3 or so brews we have allowed to sit that long in primary fermentation.
This off flavor mellowed with time, but contributed to my two least favorite brews in my time brewing. The total was 10 gallons pale ale, 10 gallons Belgian strong, both recipes I had brewed before.
I can't defend all the reasons, but in my circle of brewers, we avoid going much more than 2 weeks in primary, all things being equal.