There is no inherent reason why both DC generators and DC alternators couldn't self build their fields without the help of a battery... But in practice, economics doesn't allow that to work out for DC alternators. The problem is the result of the electronics needed to regulate the voltage and to rectify the current coming out of an alternator.
In the days of generators, regulators were exclusively electro mechanical. When the voltage coming out of a DC generator was too low, the relay contacts that controlled the field were closed, and the reverse current relay was open so that 100% of the residual voltage coming out of the armature went to the field. If the field resistance was high enough, so that the field current didn't swamp out the residual power coming out of the generator, it would essentially lift itself up by its boot straps, slowly at first, and the voltage and power would rise until it was self sustaining.
The DC alternator has never had that luxury. Because the field needs to be DC excited, there has to be some method of converting the residual AC voltages that come out of the stator windings to the DC needed to excite the field. The problem is the very diode rectifiers needed to do this waste a lot of the available residual AC power needed to let the alternator self excite. Each stator winding has two diodes in series with its output. That wastes about 0.7V for each diode, for 1.4V total.
The problem is compounded: In DC generator systems, there needs to be a way to disconnect the generator from the battery so when the engine is stopped, the battery won't drive the generator as a motor. DC generator regulators had a reverse current relay that preformed this task. If the generator wasn't putting out sufficient voltage and current, in the right direction, the relay would keep the generator disconnected from the load. DC alternators don't have this relay. They use the diodes that rectify the stator currents to do the task. As a result, any current the alternator tries to make with the residual magnetism heads straight into the electrical system, and is gobbled up before it can help the field winding build.
And to further complicate the modern DC alternator's life, it has an electronic voltage regulator that needs a certain amount of power just to make the transistors in the regulator switch on so that the current made by the residual field magnetism can pass to the field windings and help the alternator self excite.... the camel's back has been well and thoroughly broken!
With the addition of a reverse current relay, and a direct excitation path from the stators to the field, a DC alternator could be made so that would self excite. But the car manufacturers don't see that as being of any value in a system that already has an expensive rechargeable battery, so they aren't willing to waste the money, space, weight, or power that such a circuit would take.
Self exciting portable gensets, are a different subject entirely. Because they have no battery by design, they have the direct self-excitation circuit built in. They also have no regulator, they rely on the non linear magnetization characteristics of the field to reach an equilibrium that is close enough to run normal AC loads.
More than you wanted to know, I am sure.
-Chuck
