Yeah, both of those guys got on fine with just one bass, but they played motown and country and those kind of genres where a p-bass with flats is exactly the thing you need, but what if OP ends up playing something completely different like hip hop of even something crazy like djent, good luck playing djent on a p-bass with flatwounds.
At the same time I think about that not every bass can play every type of music, I also think flatwound strung P-Bass can play almost anything not only motown and country (?) music like you said.
But the underlined points from my comment above are:
1. Not everybody has to be a Versatile bassists. Although it's ok too if somebody would like to be.
2. Not everybody has to buy/have any kind of different gears & basses, strings, fret/fretless etc. Although it's ok if somebody would like it too.
3. To do what you call as "Sessions and High Level Gigs", a bassist doesn't always have to be a versatile kind of player nor have many kind of different basses & gears. Infact, most of the time, people (producers, MDs, etc) call a bassist not because his/her versatility, but because of his/her SPECIALITY instead. Although of course there are also 'places' for versatile (type of) bassists.
4. Again, P-Bass with flat wounds clearly can do much more than what I think You think it can, looking at how you write your comment above. Although for some people, it is impossible to do anything.
I play, record, produce, MD for hip-hop music too. With my flatwound strung P-Bass. It's sweet.
Of course anybody can choose what is good for them, and can do anything with anything they like, e.g. playing hip-hop with Fodera, etc..but as I said,..anybody should be able to play anything with anything he have. The result might be different, but not necessary bad.