Interesting. And your theory seems to hold water: V=IR, so with constant voltage, current is inversely proportional to resistance, and the resistance of 100 bulbs in series is far far greater than 100 bulbs in parallel.
Your intuition is correct, but a minor nit: bulbs aren't linear devices and don't have a fixed resistance. At low power, a bulb will look pretty close to a short circuit (it's just a piece of tungsten wire, after all). As power increases, the filament temperature rises and so does its resistance. This is why bulbs generally burn out when turning on - 170V across a mostly short circuit, with most of the resistance being in whatever section of the filament is most worn through, so most energy is dissipated at a single spot. poof!.
The nominal voltage on an AC power line refers to the "RMS" average of the waveform. The peak voltage of a sine wave is sqrt(2)*RMS. Presumably bulbs tend to blow when they're turned on while the voltage is near a peak.
Apart from other reasons mentioned. LEDs don’t work well in parallel. Even if you have just 2 of them, one will be bit brighter (drawing more current) than the other.
It requires 20 inches of wire in both cases. When connected in parallel, each socket acts as a pass-through to connect the hot and grounded wires to the next socket in the set, in addition to providing power to the bulb. Thus, the sockets are in series but the bulbs are in parallel. This is how electrical wall outlets are wired.
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.
Why would you need a separate wire for each bulb? Seems to me like you could have a ladder topology: two bus wires running from the outlet, and then the bulbs going between them.
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.
Interesting: That would suggest that if you let enough bulbs on a strand go out, you reach a cascading-failure threshold at some point, where the voltage across the remaining filaments is higher than their rating. And then I guess the breaker trips.
Yes, if you shunted enough of the bulbs in the strand you would get a cascading overvoltage down the line. It wouldn't trip a conventional breaker, though. Those bulbs can't pull enough power, even in over-voltage conditions. Might trip an Arc Fault Circuit Interrupter, though.
Higher voltage on the remaining filaments really just shortens their life. So yes it's a type of cascading failure, but it's not catastrophic (each set has a fuse in the plug anyway, otherwise that 28AWG wire would function as the filament of last resort, if you get my drift).
This means you want to replace burnt out bulbs when you notice them, rather than waiting for the whole segment to go dark.