I suspect from your post you have not flown any actual intercepts. Intercepting any target at high altitude and Mach is very difficult. It would be almost impossible if you did not have a huge thrust and speed advantage. Most intercepts are done from the forward quarter and it takes very careful coordination to time a intercept turn and join on a target cruising at .83 Mach. In most cases the interceptor is also climbing. It takes tremendous power to sustain a 3G turn at 35000 feet while climbing. Running down a target from behind in a jet only capable of .9 mach would take forever if you elected a stern conversion.