Waste of money or not Mike, both caused problems for the Brit and US forces in the UK at the time. More importantly, the V2, as already mentioned, could not be countered (once launched), and announced its presence after it had exploded - with the double 'boom' of its sonic bang being heard seconds after it landed and exploded. In that respect, it was the most deadly, no matter how effective, or not, it could have been in the long term.
More importantly, it was the first opening of a brand-new chapter of warfare - the missile - which was undetected and, even if detected, could not be neutralized.
Ever since then, with this first 'sortie' into guided, targeted weapons, man has lived under the cloud of more 'developed' systems, which, don't just travel 200 miles from the launch site, in a tactical situation, but can travel across half the globe, with much more devastating results.
Thank Heavens von Braun and Dornberger spoke to the 'western' Allies first, after WW2 !!