They could just convert the prize money to BTC today, advertise it in that currency, and not have to worry how the market changes?

Problem there is that you're exposing the participants to volatility risk. if btc drops in price then people might be less likely to participate. Many view bitcoin as a great new technology but its price is still too unstable to actually quote products/prices/prices in. Quote in dollars, delivery bitcoin and everyone wins

I guess I imagined that being exposed to volatility risk is something that anyone involved in Bitcoin came to terms with a long time ago.

Yes, but the smart ones learned to minimize their exposure.

Where would they find a secure way to store BTC? They've probably heard about the recent difficulties....