I agree Chris, Marcus would still sound like Marcus whatever he plays and I would still sound like me on his bass.
I think also along with the bass that a player uses, it is also the note choices and how they are articulated them that makes a players style recognisable so it's more than just the sound an instrument brings with it.
True, you don't need an expensive bass to be a great player. I would confidently assert that most of us learnt our craft on pretty dodgy, cheap basic instruments and only when we got to a competent level, and finance allowed, chose to purchase an expensive or quality instrument.
It would be an interesting test to get a band of some top musicians to record/perform on stage completely using beginners starter instruments and back line, everything from brass, to drums, guitars, amps, mics, cables cabs, keyboards, the works, taken right from a shop without any modifications adjustments or anything. Just tune up and go. I wonder how much different the overall sound of the band would be?
Jazzyvee