Commentary: The show must go on, right?

My recent Nightwish concert review mentioned the drama centered around last week's Denver show.
Heres the recap: Lead singer Anette Olzon fell ill and spent her evening at the emergency. Tuomas Holopainen polled the audience on whether they should cancel the concert. The end result is that the two female singers from Kamelot sat in and Nightwish adapted their set the best they could. Apparently after this, Olzon was upset and believed they should have cancelled the show, because it's not Nightwish without her. Now, Olzon has left the band.

I'm not interested in picking sides or trying to sort out Nightwish's band dynamics in the wake of the split. The more interesting thought is whether Olzon was right about cancelling the show. On the surface, it's a bad idea because it would cost the band a lot of money and good will, both with the audience and the venue. But Olzon has a point that losing a vital player could kill the show.

In the Nightwish case, I voted along with the rest of the audience to let the show go on, even though I was disappointed about missing Olzon's great voice. But how would this play out with other bands, if a key member couldn't make the show that night?

Let's skip the easy ones, like a White Stripes show without Jack White or a single name artist (it's hard to see Peter Gabriel without Peter Gabriel). The band should have a chance of satisfying their fans despite the handicap. But the math gets interesting.

What about Tenacious D without Kyle Gass? Jack Black dominates the duo with an outrageous personality. But Kage brings an understated balance to the show that grounds Black's exuberance. While I'd love to see JB do a solo show, it wouldn't be Tenacious D without Gass. Similarly, it would be hard to stick it out with OK Go if Damian Kulash or Tim Nordwind had to cancel.

A mathematical approach would suggest that each member could be assigned a score and if they were subtracted from the band's total, the show should be cancelled if the remainder would be too small. But the Tenacious D and OK Go examples bring up a kind of synergy, created by the interaction within the band.

In those examples, losing the front person/lead singer would certainly kill the show, but losing another strong personality in the band can still make the handicap too big. On the other hand, if there's enough charisma or magic still there, it could tip the balance the other way. Seeing King Crimson without Adrian Belew would be a disappointment, but I'd stay for that show. ...And You Will Know Us by the Trail of Dead would still be worthwhile if Conrad Keely couldn't make it.
As I sit here thinking about different examples, the one that surprised me the most was the Rolling Stones. If I were at at Stones concert and they announced that either Mick Jagger or Keith Richards wouldn't be there, would I stay for the show instead of getting a refund? For most, the answer seems clear: if Mick's gone, it's not the Rolling Stones at all. Many if not most would feel the same about Keith. But the more I wrestled with this one for myself, I settled on the non-intuitive result: I'd stay if either were missing, in part to see how much of the magic remained.

Which bands come to your mind and where would you draw the line?