Wow, I didn't think of the angle that the EBay sellers come out in force and look for autographs. That does indeed seem to be a good reason not to sign unless someone has seen the show.
However, I can imagine a situation where someone has previously seen a show but couldn't meet the actors that time for whatever reason. My guess is that, if the autograph seeker explains the circumstances, the actor would sign.
I went to a Civil War reenactment where Jeff Shaara and Tony Horwitz were selling and signing their books. I only bought Jeff's book because I already had Tony's at home. I asked both of them to sign Jeff's book because, as I explained to Tony, I absolutely adored "Confederates in the Attic" (Tony's book) but didn't need a second copy. I was really friendly about it, so Tony smiled and signed Jeff's book. It was absolutely clear that I was being truthful, because I mentioned some parts that I really loved. It also helped that the table wasn't mobbed, the way a stage door would be.
Finally, both sides have valid points in this thread, as in most. I really wish that folks would tone down the personal attacks.
You alone can make my song take flight.