Why bother with a new airframe then? Just work out the systems in a current, effective airframe like the F-16 or -22.

But as stated elsewhere, that isn't porky enough.

It doesn't necessarily follow from "the airframe isn't the most expensive part" that you still wouldn't want an improved airframe.

The F-16 isn't stealthy (terrible in fact), and the F-22 isn't well suited as a strike bomber - its weapon bays are too small.

In fact, the F-35's single engine design works well in providing enough space for weapon bays, while still keeping the aircraft fairly compact.

The airframe dictates the missions.

The F-16's airframe is fine, but not stealthy. Stealth is crucial when it comes to taking out the tracking radars of most "strategic level" SAM systems (like the S-300 and S-400). The F-16, with its inability to carry stores internally, shines like a beacon to these SAM systems and can't get close enough to take them out without huge amounts of support.

Thus, the F-35.

There are some airframe advances, but they indeed are producing F-15 and F-16 still.

I don't know why I was downvoted with no good counterarguments.