We all have to compete but rather than disparage a business owner for being a good steward of their money could you instead present a valid argument for using a designer as opposed to a contest? Some good reasons why a designer, that might hypothetically cost 10x more than a contest, would be better money spent in the long run, would offer a lot of value to this conversation. I feel like the last quote in your post is valid. Why would someone want to pay a lot and possibly get nothing for it? Is that not a waste of the business owner's time and money?
I'm not trolling. As a business owner on a limited budget and with clients in the same boat, I'm genuinely interested in the answer.