So why even design it to do a mediocre job of dogfighting when they could equivalently eliminate that design constraint and allow it to do its other roles better?
From what I've read, the F-35 was supposed to excel in all roles. It's supposed to be a bomber, fighter, be useable from flight decks as well as airports, etc...
I understand that. That's the exact problem. To me, the F-35 issue represents a case of politicising the systems engineering process.
All of the defence contractors are really good at implementing systems from requirement specifications. In this case, the requirement specification has been added to and added to by political desires until it represents an object that simply can't pass muster. Lockheed has some incredible engineering talent, but even they cannot implement a system that has specifications simply unachievable by current technology.
Something has obviously gone horribly wrong with the requirements capture stage of the program. The program sponsors (the military) have clearly asked for an impossible task. That's been bundled up in a specification and passed to engineers, who despite their best efforts are simply unable to make all the components play nicely together. Now we have a broken system because the subsystems just can't fit together. The textbook example is the VTOL aspect - a sleek and aerodynamic fighter can't afford to have a whopping great rotating turbofan in its guts, yet the requirements are both there.
If this isn't taught in systems engineering classes in 10-20 years as a case study on what not to do, I'll eat my hat.