Alcohol makes a great preservative... which, in case you forgot, is one of the big reasons that beer became popular to begin with.
What made beer popular to begin with was not alcohol's preservative power, but rather the psychoactive effects of ethanol. For the first 4500 years of beer production, most brews went sour in less than a week despite their alcohol content.
Refrigeration was the most important preservative for beer. That and
germ theory leading to better
sanitation.
How well a beer ages doesn't just depend on infection, though. The off-flavors contributed by yeast cell autolysis is what you have to worry about when leaving a beer on the yeast.
OK, I've read all this. What's sitting on the bottom of the bottles when you carbonate with a sugar? Isn't that a little yeast cake! If you scale that to a keg size it's a fair bit. So, bottled and stored in the shed, why hasn't the beer gone sour after twelve months in a bottle? Most stories I hear and read, beers get better after that sort of time.
(just askin')
Again, yeast cell autolysis doesn't make beer go sour. That's due to the presence of other microbes.
Yes, the yeast cells in the bottom of a bottle are a little yeast cake, but here's the difference: A lot of the yeast on the bottom of the fermenter is gimpy and on its way to autolysis. When you bottle, you're only picking up yeast still in suspension. Generally, these are very healthy yeast. So bottling is a kind of Darwinian 'bottleneck' (pun intended) which selects for healthier yeast, less likely to undergo autolysis any time soon. So aging on those yeast in the bottles is a lot less of an issue, though they will eventually die and rot away down there, despite the presence of any amount of alcohol, contributing off-flavors to the beer, though that might take a year or even more as opposed to a few months.
The long and short of it is this: after about a month on the yeast cake the flavor benefit of those yeast being around starts to become a flavor liability. If they are cooled down, you buy yourself more time.