So why aren't the bulbs hooked up in parallel?
LEDs use less power but don't work well in parallel.
With 10 bulbs at 1 inch spacing, you're wiring 1 + 2 + 3 + ... + 9 + 10 = 55 inches of wire instead of 10
Follows a roughly N^2 law
Like this: http://www.planetchristmas.com/Images/MinisA.gif
I think the real answer is that if you did it this way (in traditional pre-transformer light sets), each bulb would have to be rated for 120v, or whatever your local line voltage is, which would make them both more expensive, and more dangerous.
This means you want to replace burnt out bulbs when you notice them, rather than waiting for the whole segment to go dark.
Edit: Sorry, I misread, I thought this subthread was about parallel circuits.
If half of them burn out (and, as the article explains, become a short-circuit), then you have 50 bulbs, and each is getting 2.2V across it.
The problem is that a parallel connection requires bulbs that can take 120VAC directly. This is not a problem with C7 and C9 light sets (the small Edison base bulbs). The minis, though, can only take a few volts. Thus, they need to be series-connected to get the voltage drops across the individual bulbs to the level a single bulb can handle.