I'm not seeing any mention of my own issues with Fenders in this thread, which is making me think that I'm way off base, but...
Both P and J basses have always seemed a little, well, chunky (both literally and in their style of construction). Over the decades, couldn't Mr. Fender/FMIC have lightened the body (maybe chambering it?), or figured out a less blocky way to attach the neck to the body? I love the sound of Fenders, and enjoy my fretless MIM J, but I usually play sitting down and also wish the trademark headstock was reduced 10% or so, with some lighter tuners. Now that I think about it, I guess I wish the whole instrument were slimmed down/shortened by a few percent. I feel like I have to adapt my body to the shape/size of the bass, rather than the other way around.
That said, icons become icons because they captivate people and work well enough to satisfy the majority of customers. It's not like a first-gen Ford Mustang is perfect, either, and the Eames Recliner has always seemed too low and fragile to me. Fender basses work really well, despite the issues. That's why we all end up with 1 or 7 of them, right?