The concern about whether "competition" will corrupt Aikido is difficult to address in these forums because without first hand experience with the Shodokan method and its culture people have a tendency to project all of the failures of competitive events onto it. For instance "it's very common to see winners jump and strut like peacocks around the arena, with a savage happiness in their faces, whilst losers get out absolutely dismayed." Now, that makes good copy, but it does not accurately reflect the experience of Randori Shiai. I would caution against people making sweeping generalizations about something they have not experienced. I would also suggest that while some events are like that described, many more are not.
For the record, I studied "traditional" aikido for years before finding my present teacher/dojo. The main reason I switched was the dramatic difference in the egos and posturing, with the Shodokan stylist being much less ego-driven and, oddly, less competitive. That's just my experience and I am in no way saying this is a global problem/situation.
One of things about having our type of randori is that it gives you the opportunity to face "contest" and measure our aikido and ourselves against it. Now, "the desire to win at all costs" will not get you very far, I assure you. In order to play successfully you have to have a deep and immediate understanding of aikido principles and dynamics. You have to be able to transcend the willingness to win, to "make something happen" and have to find a way allow the aikido to happen.
You also need to be having a good day;^) As part of regular training mudansha get the opportunity to play above their heads and yudansha get to be reminded that rank and history are no match for taking your opponent seriously. You also are provided with an opportunity to face a "won/loss" scenario head on and take it for what it's worth. Wining is not always the best answer or the best teacher and that is definitely re-enforced in my personal experience with the form.
As far as competition never happening, well, too late. Not only are there events in the states and through out the world but there is a particularly virulant strain active across Japanese college campuses.
Concerning the Olympics, Sam, you are correct about Kendo and thanks for reminding me. And let's face it, what sort of chance does Akido Kyogi stand agianst Kendo?