Engines - That's pretty close to how it happened, with a few caveats.
Anyone who thought that simply mandating single-seat/single-engine would automatically constrain costs was being simplistic. There was a hope that the JSF would be in the Classic Hornet weight bracket but it went out of the window pretty quickly, with the result that the aircraft is in the Super H class, nudging up against the F-15.
Of the technology enablers, the lighter-engine bit did not pan out and networking could be built into any platform. However, a very important enabler was the "every weapon a precision weapon" concept of JDAM, which was well under way by 1996. This was what allowed the operators to accept a basic two-bomb internal load (down from 12 klb in the A-12, about 6-8 klb in AX and 4 bombs in A/F-X).
Also, while F-35B is sold as maintaining the Marines' sea-based air and their ability to operate off any 3,000 foot stretch of runway that has a 100-foot-square slab of continuously reinforced refractory concrete next to it, it's actually replacing the F/A-18 Classics first.