Hmm.. I've got 22 in my collection right now. It used to be -alot- more. Do I need 22? Absolutely not. But some are players, some are investments, and some are just art.
I don't think you necessarily have to think that it should sound VASTLY different. It's more about what role it fills. For example, I wouldnt play a semi acoustic in a metal band. Now, that role could be defined by something as simple as looks. Looks SHOULDNT matter, but it definitely does. It's part of the band image.
Other roles could be one thats more comfortable for long sets, one that has more bite, a silly one for a certain song, a extra long/short/extra frets for certain songs. One you can keep in a certain tuning, etc.
Tbh there are as many reasons to buy a bass as there are basses.
But going back to sound, I think pretty much everyone who plays a music semi/professionally can agree that TO THEM, each one sounds different. Wether it be keys, different dimension drums, mouth pieces for horns, or basses for us bassists. It doesnt necessarily sound different to the audience, but thats another thing alltogether.
I have certain basses for certain songs/bands/tunings etc, which, IMO, all contribute in their own way to the vibe/completeness of each song/band.
But this is just me.
Anyway, I am a firm believer that all bass players above intermediate level should have atleast 1 precision, 1 jazz, and a hollowbody/semi acoustic. Preferably 2 of each; 1 with flats and 1 with rounds.
And thats before even getting into stuff like pickup placements on the hollow, scale, and all the other factors I mentioned.
All that being said, I do have 1 go-to bass that will fit most situations. That's a jazz. That's the one I will always bring to rehearsals etc, atleast the first few times. For live settings, I will bring atleast 1 more, either for the reasons stated above, or just as a backup, incase something happens.
Hope that helps