It depends on the bassist.
If you change the pick-up settings for different songs to get a different tone, that would be a convenience rather than switching basses. If the tone you want doesn't require a different pick-up, then probably one pick-up will do.
My first bass only had a split pick-up and my second only had one split pick-up. I didn't like that it only had one tone that I could vary slightly with the tone knob.
Playing basses with two pick-ups at a store, I see I can get a wider variety of sounds.
Considering I've only played bass in a church setting, I found my bass tone was adjustable by the tone knob on my bass and the EQ settings on the amp.Church music runs the gamut of music styles in one set, country, gospel, rock, jazz, soft rock, alternative rock, reggae, adult contemporary, pop, 80's rock, modern country, country western,etc. Changing EQ settings on the amp on the fly between songs was not doable. No one really noticed anyway because it was the bass. Low frequency and all. Even though it's not a secular rock music setting, the bass player is still an invisible man to single women. That was a side note. I am hoping in the future to get a Carvin SB4000.