It depends! :-).

In a cover band, I think you need flexibility in your tone to at least approach the tones of the originals, unless you've taken the approach to put your own spin and sound on the tunes!

For original material, certainly you should find your tone! You tone should be one that inspires you and propels your playing. It becomes part of your signature sound. That's because part of your tone comes from you...your hands.

I've found 2 tones that really inspire me. One is my strat on the neck pickup through the clean channel on a tube amp. More recently, I have found my Les Paul on the bridge pickup through a tube screamer to be really inspiring. It can be sort of mellow, but if you crank it and start digging is, it can, well, scream!! SRV loved his tubescreamer...if it was good enough for him... :-).

I can see myself finding at least one more tone for heavier stuff. I've been dabbling with the Dist+ pedal for this.