Yes, as I'm sure we're all well aware, first generation guided missiles were crap in all kinds of ways. But they don't need to be as good as guided weapons anno 2024, they just need to be enough better than the unguided systems they would replace/complement to be worth the extra cost.
Never said they had to as good as the weapons of 2024. I said and bolded 1955 for a reason (or several), it is 10 years after the end of WW II. It is within about 2 years (give or take) of many guided missiles systems actually being deployed. Not tested or even field tested, large scale deployment. And for AA missiles over 1/2 of the ten period was under the threat of atomic weapons which put more urgency into development compared to the 3-4 years post WW II.
Take the SAM; it needs to be more cost effective than heavy AA, it doesn't need to achieve anything close to "one shot one kill". German heavy flak apparently needed around 16000 shells for every heavy bomber they shot down, an astounding number when you think about it. And not only the shells, that's quite a few barrels worn out as well per kill, a huge amount of manpower to crew them etc. Even if the SAM's would achieve no better than a 10% hit probability it would still be a huge improvement. Heck even with a 1-in-50 hit rate it would probably still be cost effective compared to heavy AA.
The number 16,000 is often quoted but it is a bit disingenuous. I am not referring to you but by the people writing some of the articles/papers. An 88mm shell weighed 20.7lbs and used 5.3lbs of propellent.
German Wasserfall weighed 8200lbs and weight of propellent (different) was????
Soviet SA-2 weighed 5200lbs and propellent was ???
SA-2 consumed about 200 times the resources of an 88mm round (a little fast a loose here, a lot of steel vs some aluminum and so on) The Wasserfull was worse.
The Wasserfall guidance "system" well and truly sucked. As with many German wonder weapons, an improved guidance system (like one that could be used at night or one that could be used in a slightly cloudy daytime sky) was "under development".
SA-2s achieved kill rates of between 1 in 10 to 1 in 25 (?) depending on conditions (ECM status and others) using nor only radar far in advance of WW II but also propulsion technology and computer technology (analog) far in excess of WW II. Ten 5000lb missiles = 1920 88mm shells. Still better but not the disparity many writers claim.
Figure in the support systems, like the number of radars/radios and the analog computers to make the system work.
The AA missile was a better deal, but it took a huge amount of work to get it to be effective (even for 1 hit in 10), when did the regime change happen? In WW II the AA missile was marks blazed on trees showing the way forward but there were a lot of cold camps and missed meals before home was reached.