OK, in that case I see the point of fighters as a secondary line of defense for the AWACS. If the AWACS can stand off so far, however, then the primary weapon could be just a mobile missile platform, relying on the AWACS for targeting info. That seems easier and cheaper to build than whatever the F-35 has become.

To a certain extent no-one knows for sure, because there's never been an all-out war between modern air forces. The go-to example for a lot of the doctrine is the Falklands war which was over 30 years ago. That said:

To a certain extent a modern fighter plane is just a missile platform. You want your missile platform to be fast and stealthed, and you want it to be able to fly close to the ground to make it harder to detect, which means making it maneuverable and at current technology levels probably forces it to be piloted. You want the survivability stuff - ECM, flares and all that.

At that point you're most of the way to having a modern dedicated fighter (like say the F-22). Could you leave off having detection equipment on the fighter itself? Maybe, but that would severely limit where you could operate - AWACS planes can't really operate in disputed territory (they tend to be modified civilian airframes, they don't have any of the things in the previous paragraph, because they want to carry large bulky radars). Radar and the like is a relatively small addition and opens up a lot of other mission possibilities - either escorting bombers in hostile territory or, these days, taking on a bombing role itself (modern fighters are large enough, and modern missiles heavy enough, and modern precision bombs light enough, that it seems like every modern fighter has at least some ground-attack capability). Interestingly enough the F-22 goes in the opposite direction - it's been described as a "mini-AWACS" and can provide targeting information to friendly aircraft.

Is it then worth using the same plane for close air support? It's arguable but IMO that part also makes sense. It's the STOVL requirement that really kills the F-35 - cut the lift fan, narrow the fuselage and you'd have a good aeroplane (which would still have software problems, but I'm not sure building multiple aircraft would have gone any better on that front).