I don't want to imply I am referring to that specific search engine, but paid search engine inclusion to me seems like little more than a scam. What possible benefit could there be in that, and why SHOULD I when Google indexes my site for free and sends me thousands of relevant visitors?!

I got that offer too - from when I did a search engine submission blast to see how those things work. Half of those so-called search engines make you opt in to get your site included and most of those try to charge you to fast-track you. Well, kudos for trying I suppose, but I will be politely declining that offer and all similar ones!