Even Space Shuttle later was driven (and funded) heavily by military applications, a lot of Apollo funding came from wish of improving missile guidance systems

Even Space Shuttle later was driven (and funded) heavily by military applications, a lot of Apollo funding came from wish of improving missile guidance systems as well. You're trying to make a distinction where there is none - it's the same bag of money. Which also why the money quickly dried up when rocket guidance, indeed, became a solved problem. Before Apollo was finished.