The voltage regulates itself. Simple as that.
You are aware that, unless explicitly designed with additional peripheral hardware, all batteries are unregulated power sources, right? By your argument, the simplest form of active regulation (aka buffer) serves no purpose.
In that example battery linked above, the impedance is listed as 3 milliohms.
That specification is given under controlled laboratory conditions and is pretty much useless for all practical purposes. Like I said earlier, internal resistance is a
dynamic parameter and a function of
multiple variables to include load, temperature, internal design, age of device, etc. If we assume that internal resistance remains constant or even doubles, then sure, it's relatively insignificant. But it won't. In fact, a 100-fold or 1000-fold increase in internal resistance isn't uncommon. And just when you think you're done, there's feedback consequences in the form of internal heat dissipation which will exacerbate the situation.
Also, since the original requirement didn't specify any tolerance or allowable range for the 300 V output it is impossible to say whether any actual range of output voltages is or is not satisfactory.
The comment "3KW nominal power output" suggests some form of regulation. Admittedly, the point is moot.
This is not so. The voltage drop as a percentage of output voltage will be the same with one battery as with 25 batteries. Hence 30 mV in 12 V will become 750 mV in 300 V. Just as insignificant. As I said, when you put batteries in series then series resistance, whether internal or external, is a constant factor.
Once again, a battery's internal resistance is not a constant parameter and will increase under various operating conditions and over the lifespan of the device far greater than you might think.
It makes perfect sense in terms of the requirements. If you reduce the number of batteries you will need a DC-DC voltage converter of some kind to get the 300 V output, and this will increase the current draw on the remaining lower voltage battery supply compared to the 25 batteries in series for equal power outputs. Like for like, fewer batteries demands more current from each battery.
Naturally, by argument of conservation of energy. However 1) your sol'n does not include a transformer or any other form of DC-DC converter, and 2) the comment made by Psi was originally made in the context of batteries in parallel, of which your sol'n does not include.
As an aside, I could have sworn Dave did a blog some time ago on the topic of batteries.