I started playing bass with a Fender P, and I played that bass exclusively for more than 2 years. Being a noob at the time, I dind't know anything about the classic "P with flats" combination, I just tried different strings and immediately fall in love with the sound of flats. The combination of the simplicity of the P bass and that deep thumpy tone simply WORKS, there's not much to say.
My "problem" with flats and J basses (even more with StingRays) is that they seem to reduce their versatility, imho.
The beauty of these basses is that they offer a wide range of tones, they work very well for slap and many other styles. Flats reduce that range, in my experience.
Honestly, I can't see myself using flats on my StingRay, at least not at the moment. But I know how well these strings sound and I'm curious to try them.