Is there a way for us to waste GoDaddy's money by searching for domain names that we don't actually want? If they waste enough, they'll have to stop this practice.

They're probably not buying every domain that's searched, but if you appear likely to buy the domain by having an existing account, only searching for a single domain that's based on an english word, and getting most of the way through the checkout flow, that might trick them into buying a garbage domain name.