Add to this the complex microadjustments of aperture size and lip tension required to ensure you get a clear high C rather than a quiet D (or loud Bb!), all of which have to operate in synchrony without you having to think about them, and you get some idea of why relatively small improvements in range take many months of properly structured, regular practice to achieve.
This is where lip slurs really come into their own. As a regular part of your practice routine, they both build the embouchure strength, and over many thousands of repetitions, lock in the muscle memory so that you can replicate the exact physical set up required for that note no matter what distance and direction you approach it from. Oh yes, and you have to get your abdominals working in synchrony too. And I'm not even going to mention the tongue. Oops.