The airplanes aren't just a platform for missiles. They are an integrated weapons system. The weapons integrate with the high tech electronics on board the aircraft. Weapons like the AMRAAM use the aircraft radar system to guide the weapon close enough to a target to acquire it on the missile's own radar system. You can't just strap a missile on a WWII fighter and have it work.
There are a lot of planes out there that are as good or better than the F-15 (The F1 and MIG 29). There are also a lot of high tech SAMS out there that are a threat to non-stealth aircraft. That's why we need a stealthy fighter and not some WWII Antiques. Also, the more planes you have the more support personnel you need to keep them flying. You need about 14 people per aircraft for maintenance and each of those folks need to get fed, paid, etc. There comes a point when you reach a diminishing return.
The idea of using a lot of cheap planes isn't really viable because you need a lot of expendable pilots to fly them. The US Air Force philosophy is to use fewer aircraft with better training and technology. We tried it the other way during WWII and lost as many as 60% of the aircraft on a single bombing mission.
But perhaps you CAN use one or more UAVs to fly along WITH the fighter to supplement its missile load with missiles that can be launched from the UAV but guided by the fighter's electronics