Bicycle dynamos are perfect just the way they are! The design is super simple or KISS (Keep It Simple Stupid) so there reliable for many years with no brushes to replace or commuters to clean as would be required with DC generators. AC current will travel thin wire long distances where as DC current will be absorbed and turned to heat by the copper wire requiring larger wire be used. Adding a bridge rectifier consisting of four 1N5818 diodes is a cheap and simple way to obtain DC from an AC source.
As a general rule, bike dynamos are indeed very simple and reliable. Nothing to wear out, such as brushes.
The reason why AC power generation and transmission is preferred over DC is a little more complicated that the explanation by n4zou, but power loss is the heart of it. With DC power, the voltage is limited by the risk of killing the customer. As the voltage is lowered, the current required to deliver a given amount of power increases. If you want to deliver 100 watts at 1000 volts, only 0.1A needs to be delivered. If you limit the voltage to 100 volts, then 1 A is required. Since losses in wire are equal to the square of the current times the resistance, the 10 x increase in current results in 100 x the power loss!
The advantage of AC power is that transformers can be used to increase the voltage to very high levels (around 14,000 volts, I think..) for transmission over large distances. When it gets closer to the customer, other transformers are used to drop the voltage down to relatively safe levels.
Wonderful stuff, but not really relevant to bikes. AC is used because the dynamo is simpler, and incandescent bulbs really don't care whether they are powered by AC or DC. LEDs do care, and as mentioned, the bridge rectifier is a simple and cheap way to convert to DC power. If efficiency is a high priority, schottky diodes can be used, or even a bridge made of mosfets (very, very low losses).
Steve K.