Right, they haven't, and they won't. But we know NG and GD aren't going to, Raytheon comes next on the list of biggest contractors. The rest is far off or doesn't have much to offer and it's not exactly something a start-up can do, hehe. I'd say Raytheon is best bet if there's going to be a new American player. They probably would need to do a few acquisitions though. Honestly though, don't see it happening in my lifetime, but it's not like we're going to see new startups or the smaller defence companies coming to compete with Boeing. Unless there's real innovation for fighters... but then it's probably not going to be manned, nor big.
So light fighter with single-engine modern equivalent of what was F404 but with AESA radar and true multirole capability including EW and recce... you do know we've already got a modern F-20, right? It's called Gripen NG. Not light enough, then FA-50 comes to mind. A light fighter deriative of the T-50 Golden Eagle. So we've already got it, there are new players, they are just not in the league. So what you need then is a US contractor that will take these and turn them into US offers, ow dang, we know how that's going to work out... ouch: US101, C-27J, KC-30, A-29.
However if with "modern copy" you mean stealth and internal weapon carriage, then I'm pretty sure that it will bloat to become another F-35. Not that an alternative would be bad. But I bet there will be nothing left of the "F-20 inspiration" so to speak.
Other than all that, sounds good to me. There's a lot of countries out there with F-5s on their last legs and cash-strapped F-16 operators, and these are now almost forced to get "exotic" in terms of suppliers or overspend on fighters that are frankly way better than they needed and far too expensive to maintain/sustain. At the end of the day for the majority of countries, all it needs in added capability is to be able take down or scare off a Flanker or two and guide a few bombs. Then it will already be a huge improvement over its predecessor and be good enough. For countries with bigger requirements/ambitions, I really believe in mixed fleets, but clearly mixed fleet of two overly expensive types isn't the way to go (ahum, with a few exceptions, but maybe in those cases a low-med-high mix would be better than low-high capability where low means great and high super capable).
Finally, if you want a cheaper F-20 equivalent, then don't look to China. Their designs are heavy, their only cheap and light fighter is a MiG-21 copy, and it ain't that good. Or did you mean FC-1/JF-17, just ask Pakistan, can swap F-16 for one? It's really overrated in my opinion. It's overall closer to the F-20 probably than anything else, but that doesn't make it a winner. At least that's how I feel.