More realistically, Visa was probably hoping that many consumers would, like the author, already have the option of and be forced into using their Visa card.
I agree that this seems, in addition to being extremely frustrating to almost all consumers, a silly marketing move, but I'm sure that Visa has run the numbers and has a sound business reason for doing this. Since, judging by mthoms's post, this seems to be a tradition at Olympics, my reasoning may be off, but I imagine that forcing all vendors to only accept Visa must cost a lot more than a sponsorship without that condition—and I really think that they wouldn't blindly jump into that without a sound reason.
There's the obvious trade-off of how much extra money Visa makes from users who have multiple cards and are forced into using Visa where they wouldn't have otherwise vs. money lost from Visa-owners who who are pissed off. But there are probably much more subtle, long-term effects. Maybe 75% of consumers present have a Visa, and 50% of those Visa-owners feel entitled and empowered by having the ability to use their card while others are frustrated; and then there's the trade-off of the 'entitled' Visa-owning 37.5% of consumers spending more with their Visa cards over the following months/years vs. the money lost due to the 25% of consumers who didn't have a Visa at the olympics and possibly hold a grudge and never own a Visa card because of the experience. Not to mention the fact that a similar sponsorship would likely be arranged if Visa decided not to do it; for all we know, MasterCard had a clear business incentive to do this but refrained because of moral reasons, but are we (consumers as a whole) discussing how valiant MasterCard is and how much they respect us as consumers or have we all forgotten a little bit about MasterCard because everyone's talking about Visa?
Again, I don't agree with this idea; I think it's bad and annoying. But I think it's silly and a bit ignorant for all of us (many of whom have no marketing experience, and most of whom don't on this scale) to assume we know more than the marketers making these decisions because we're annoyed.