They'd have to use the gap though to actually kneecap them in that time, or else it is just shoveling money into the fire.

The missile gap for example after all was settled and done, didn't matter at all because not a single missile was ever fired off. All that money, resources, talent, secrecy, lives lost maintaining that secrecy, lives dedicated to furthering that technology and secrecy, it just has not paid off at all for anything at all when you think about it. Maybe you can argue side efforts like nuclear reactor were great or space cargo deployment, but you know you could have just dug into that stuff directly without having to collect it from the drippings of the wmd effort.