It might just be a widely held misunderstanding that the V2's purpose was only meant as a ballistic missile. But if I remember correctly it was also, and probably initially mostly, meant as a psychological and political weapon, the objective being to convince British population of the necessity to reach a separate agreement with Germany, so they could end the war on that front before moving against the Soviet Union.
Therefore the best weapon had to be frightening but not necessarily very efficient from a deaths per invested dollars measurement.
The response from the British state is also to be understood as a political move: they responded with the large bombimg raids over German cities (using plain old death-toll effective bombers), thus signifying that there would be no separate peace agreement with the UK.
According to this narrative, it sounds like the German war plan was naive to believe other great powers would agree to let Germany conquer Russia, more than naive regarding the efficiency of the V2 as a weapon.
Anyway, just a reminder that ultimately it's all about politics not technology.
A good source I can remember about the V2 story during the war, from the UK point of view, was this book:
Most secret war, by R.V. Jones