This seems unlikely considering the cancellation of the F-20 program, however, the F-20 has been characterized as "the right fighter at the wrong time". As such, I'm curious if F-20 production could be restarted to provide a cheap, easy to operate fighter to support a major war effort (in this case a theoretical conflict over Taiwan) as an alternative to more expensive aircraft such as the F-16.
Interesting, but way too late.
The F-5 was an amazing fighter for its time. It wasn't based on Energy-Maneuverability, but in many ways, its airframe and design concept do resemble a 4th generation light fighter.
However, in 1980, the actual F-5 did not perform at all against Soviet aircraft such as the MiG-21 and MiG-23. Skipping the -25, as it's on another level altogether. Most likely, the F-5 just didn't have enough thrust and enough radar resolution to beat these. The big heavy F-14 did succeed.
The F-20 prototype had a single turbofan engine that far exceeded the TWR of the F-5's dual turbojets. The issue is, this engine was meant for larger aircraft, such as the F-8 and potentially an F-16 competitor. Would the F-20 have survived into production without gaining weight?
Unlikely. The F-5's avionics were also out of date, as seen by the 0:10 kill ratio against MiG 21-25. Chinese MiG-29 and Su-27 clones are an entire generation ahead of these. More extensive sensors and armament, necessary to compete, would have burdened the F-20 up considerably.
The F-5 and the F-20 were both great. They had all the potential, in their time, and were ahead of it. The F-20 would still be a very competent fighter kinematically.
The issue of concern is avionics capability and related costs. Modern fighters have the majority of their cost in avionics. Their weight is also considerable (2-3 tons in the teens era, but probably more today), and avionics are the one thing that doesn't scale with airframe size.
If modernized to carry the same generation of avionics as the latest fighter upgrades, the new F-20's cost would be at best 30% lower than that of newest F-15 or F-16 variants. With old F-5 avionics, they'd be cannon fodder to anyone who can get at least a MiG-21bis, and that's anyone these days.
In short, the importance and the cost of avionics mean that the marginal cost of heavier airframes is less significant that it used to be. High kinematic performance and a larger armament load they offer still matter. This favors larger heavier fighters from a price/performance perspective.
The light fighter niche today is mostly occupied by the Saab Gripen and the HAL Tejas. The Gripen weighs about the same as a new F-20 would, carries modern avionics, and has been polished by 25 years of reliable experience. The Tejas is new and comes from India, making procurement less politically complicated. Any new competitor would have to offer something they don't have. And it's hard to think of something neither of them has that is feasible on a smaller budget.
There certainly is a market for a lightweight fighter similar to the F-20, combining basic low observable technology, a simple, easy to maintain engine and with good but ‘no frills’ modern mission systems. The F-20 has a lot of excellent earmarks in that respect and would make a good template to start from. As to bring back the F-20 and beginning production on that again, that’s not likely. It was quite a risk for Northrop to do that in the 1980s and cost them \$3 billion in R&D (an absolute bargain compared to the F-35’s bloated \$405 billion R&D budget) and all for naught.
Given how costly and time consuming it is to produce and maintain pilots, it seems that the future of warfare is more of the expendable drones, than cheap airplanes that easily lose pilots. Estimated at $6+ million dollars to train a US pilot.
This is in addition to the valid points other good answers list. Supporting yet another airplane type has a lot of inherent costs that a hypothetical saving of 10% or even 20% can hardly justify.
Update: a video part of which goes over expenses for different airplanes and pilots. See chapters "Economics of Unmanned Systems" and "The Pilot".