Is there any reason to have a 6+ string Bass if you don't play chords

I've never seen a 6+ player with a band play more than three notes at the same time ever.

Jaco sometimes played four notes.

The six, seven, etc. allow you to play chords with more notes in different voicings without it turning to mud. In the lower registers, you're limited to two-note intervals, and maybe a third note if it's a fifth of one note in the interval. On my six, I like chord voicings like 1-5-M6-M3 and 1-5-M3-M7.

That said, yes, you can also play it like a four-string. It's the versatility that makes it worthwhile for me.
 
Same as a fiver isn't just about a few extra notes below E, the main advantage in any bass with more strings is more notes available without position shifts, like many above have mentioned. Great for reading and visualizing scales and arpegios. Fewer shifts also means better economy of motion which means you can play faster.

Damn, I've almost talked myself into one.

Trade-offs: string spacing (hard to slap). Weight. Variety. Availability.