If the goal is to transmit power over a large distance, I can see the advantage of an alternator over a generator: more power, less loss. If the target DC load is small and very close by, would an alternator still be more advantageous in terms of power production? Is there any case where DC power generation is more advantageous to AC power generation?
There are cases where DC power generation is superior to AC.
If it's going to be transmitted by DC, and you can generate at the transmission voltage, or you can step up the voltage to transmission levels without too much loss, DC is superior.
If your load is DC, and is close to your generator (in space and in voltage), DC is superior.
Both of these assume you've got suitable DC breakers available: electrical systems are usual designed to be fault tolerant, to the degree that no single fault can be dangerous to humans. This typically means ensuring the system fails to safe, and sometimes that requires breaking the current. With the development of DC breakers even for HVDC applications, this has improved considerably: previously, it was one area where AC had the advantage: in an AC circuit, current hits zero twice every cycle, making safe circuit-breaking much easier.
- And sometimes you just don't have a choice, and the technology (e.g. photovoltaics) will only generate DC, and if you want AC, you're going to have to convert it.
When chemical/photovoltaic power generation is readily available, versus electromagnetic (based on mechanical power).
If locally you have sources of mechanical power (wind turbines, steam turbines, diesel motor, hybrid car gasoline motor, etc) you use a generator and either rectify the AC to DC (with losses) or adapt your recipient devices to accept AC, or send AC into the grid.
If you have a fuel cell, a battery bank, a solar cell, you'll prefer DC loads, and you'll need to use an inverter (lossy!) to provide AC current, or send it over long distances.
...then there are cases where you work with dual power, and then simplicity decides DC is preferred. Say, a normal car which must be able to run off batteries and off the alternator. In this case, simplicity trumps other factors; first, if you used a generator, you'd get variable frequency proportional to engine speed, then you'd need an inverter to provide AC from the batteries, and then a lot of low-voltage circuits that require DC would need rectifiers locally to adapt to AC supply. It's just much easier to rectify the supplied power and keep it DC everywhere in the car.