In my head-canon, I like the idea that the DS2 was always the goal, as the ultimate mobile centre of imperial power, and that the smaller DS1 was what they could produce in the time available to finally dissolve the senate and crush a growing rebellion. I think construction on DS2 had begun with whatever resources were available before construction of DS1 was even complete. I agree with everything that’s been said about how much more quickly the construction would be after the technology had developed and many of the problems ironed out, though. But, at the very least, I find it improbable that the Empire would have left it at one Death Star, and once one had started construction, or even after it had been designed, plans for a second, bigger, better Death Star would already be filling imperial drawing boards.

(Even though destroying a planet completely is utter overkill anyway. But I view the Death Stars more as mobile governing centres than just superweapons.)