The US comprises humans who are every bit as prone to making mistakes, as prone to falling for deception as the next guy. Drop this mentality where you see them as super humans. If your fundamentals are strong, you can give them a bloody nose. The real power of the US comes from their depth. You can beat them in a battle, but they will simply keep coming at you until they defeat you in the war. You need depth and a global reach to take on the USAF, not to mention you would be contending with their army and navy at the same time along with economic sanctions. What PAF pilots have achieved in Red Flag and other bilateral exercises is significant. It is living proof that tactics work and the US is just as prone to them. Our Mirage pilot buzzing their carrier is hard evidence of this.
This is a very single minded world view and ignores the huge variability present in any war. There are two steps to discredit this view. Step 1 shows how two aircrafts can end up within WVR range on a modern battle field. Step 2 considers what happens once you are out of ammo. Do you turn tail? In that case you face an increased risk of being shot down. If you have a cannon, it gives you the option to keep fighting.
In detail, consider the case where enemy fighters are escorting a HVT which you are tasked with taking down. It could be a cargo plane, a VIP movement, or even an AEWACS. If you consume all your missiles fighting off the escort, you are in the ridiculous situation where you have a sitting duck that you can't shoot.