I'm kind of surprised there aren't more people here who like this idea. I see so many worries and complaints about making the first approach, and a matchmaker essentially eliminates that step.
One advantage I could see over a setup is that you can be completely upfront with a matchmaker about what you're looking for and what you find attractive (and in fact it's in your mutual best interest to do so), probably more honest than you'd be with someone in your social circle who might want to set you up. A matchmaker may also be able to analyze your needs more objectively. A neutral party can often see things about you that you don't see yourself. (And personally, my family and acquaintances don't know me that well at all, not to mention having fewer people in their acquaintance to introduce me to, so a matchmaker would have at least as good a chance at finding me a compatible match. I'm only speaking for myself there, but I think the case is the same for a lot of people.)
I don't agree that it would benefit a matchmaker's business to put incompatible people together just to collect a bill. For one thing, no one would suggest or refer their services if they did that. For another thing, people tend to get frustrated and give up easily when it comes to unsuccessful dating. Hardly anyone would continue to pay for a service that wasn't working for them. Some people would give up after the first try if they didn't get it right. It's in the matchmaker's best interest to be helpful, and overall I think the kind of people who choose that profession genuinely want to do that. They find it rewarding and take pride in their work, as much as anyone else who starts a business.