I have this running joke with my pals that every time we here some generic picked root note bass line we say "Oh, that's some good P bass playin'" . Not because that all P bass players have that sound of course but because a lot of bass players that pick up a P bass have this quarter note root and fifth mentality. Which is not owed to the bass itself and transfers to other basses as well, I'm not saying it's exclusive to the P bass. My point is that there is a line between uninteresting simplicity and shredding up and down the neck. Sterotypes can go both ways, with or against the P.
I know what I'm saying isn't 100%, it's just something that I have noticed. I think part of truly commanding a bass guitar is learning to hold down a rock-solid line while adding a certain personal expression to it, instead of taking the easy option of meandering up/down to the detriment of the instrument (which is tempting, because it is fun and possibly easier than holding a true line). There's many non-P people who have mastered this, and obviously a lot of Precision enthusiasts who have yet to, but the design of the instrument seems to help this skill to develop naturally.
Part of it is in the neck. Kim Deal (from The Pixies: here) for example, is a small lady who plays a Precision with a thick neck. You can hear that, and she makes it work for her. She'll play simple but elegant lines that arguably have far more personality than faster, more complex arrangements. This is part of the magic of the Precision at least to my ear: it holds the bass player firmly in the "bass position" of the band, but within that there is so much room for emphasis. Each note can be individually crafted to express a subtle difference in emotion - even just going from one to the other, over and over - in a way that you can't always get on others.
From what I can see, what you may lose in variety, you gain back tenfold in nuance. I'm still an amateur, but this is my experience from thinking at-length about it.
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