> but no sane country would want to help their adversaries to achieve stronger offensive capabilities, which surveillance would no doubt help
This was an arms race, not a single tactical battle decision. A shrewd opponent may be able to use your new technology to internally launch development of their own. They would likely recognize that after Gary Powers you weren't performing overflights anymore. They would also have had satellite imaging, and there is some data that they did use them to image the plane during testing.
So.. you let your enemy build an expensive new toy that isn't particularly useful outside of a full scale nuclear war while you build yourself some fast new fighters and some high altitude missile technology.
Is either that, or you seemingly have to accept that the KGB could not have possibly have seen through the that titanium pizza ovens story. It's much more likely that even trying to pass this off made the entire ruse all the more obvious to them.