The rationale being that you initially build some specific functionality you can't find in the market (feature), over time rounding this out into a product and finally evolving into a business as you understand how to monetize it and where opportunity for growth lies.
You don't need to have your business totally conceived on day one. And in fact, finding where the business lies (or whether you even want to grow your idea into a business) is something you'll have a much better understanding of after a few months of being out there.
Personally (disclaimer: I run the domain search site Domize - http://domize.com) I think it's wonderful we can launch these "just a feature" websites and evolve them into products or businesses over time (or not). These 'better mouse-trap' sites are a fantastic, low-risk way of generating passive income and if you can string a few together you can potentially get to a stage where you can live off them. At the very least, you've demonstrated the kind of initiative and creativity that will provide you with a great talking point on your resume.
Let's not forget, both YouTube (embeddable video for eBay auctions) and Twitter (group SMS updates) started as "just a feature" and evolved into billion dollar businesses.
I guess if I had a summary point it would be "don't be so quick to give away your customers..."
Whereas registrars are paying 10%-20% on sales affiliates generate.
You need to think about whether you can actually beat this margin on your own, taking into account overheads like payment processing fees, customer support, billing issues & fraud etc. Not to mention the hassle of it all.
That's why Beau talks about branching out into hosting below.
GoDaddy make money off domains because they have massive scale, recurring billing, and a hell of a knack for in-cart up-selling.
Personally, I don't want to get my hands dirty with any of that!
My point is simply this: don't underestimate the value of a recurring revenue stream vs. a one-time payout to your business.
With a strong product and good customer service, you can count on a customer relationship for a number of years allowing you to amortize your customer acquisition costs over a much longer term than an affiliate relationship permits.
That said, if you've got the stomach for arbitrage, then go for it - there's a lot of potential for the right business to strictly focus on lead gen and delivery. However, I don't get the sense that this is in the OP's wheelhouse. I have a bias that those with a product focus tend to operate with fatter and more sustainable margins on the basis that its necessary to support their development of the product. Marketing organizations OTOH would never start with a comment like "look at the product I built on the weekend, what kind of a business can we build with it..."
If you want to build a business that focuses on affiliate lead-gen, then this prototype is the wrong place to start. I mean, you might get there accidentally, but its definitely the long way home.
Better yet a white label website that refers business back to the reseller or registrar and can be operated as a subdomain to the resellers or registrars main website ie suggest.registrarname.com. Do this on a monthly fee basis that is reasonable not per name registered.
"b) become a reseller or registrar so that you can fully deliver the service and collect the recurring revenue."
Reseller makes sense. Becoming a registrar doesn't. Using this as the cornerstone of an idea will never result in enough to cover the ongoing costs.
There should be a lot of value in being the first site people visit when searching for a domain name though. We'll see.
GoDaddy et al might replicate your functionality. But they won't replicate a look at the competition for the business.
Better yet, be a brokerage portal. Get registrars to bid directly for the work. You also provided curated search on "best registrar" questions -- fastest, reliablest, fewest / most stolen domain problems.
If you can work out some means of obtaining good names held by squatters, that's better still -- and a real value add that would be harder to replicate. (I actually have some idea along this line.)
Why try to run a registration business when you're already good at generating traffic?
relying on the affiliate model feels like a betrayal in the UX and it essentially hands over one of the most obvious ongoing revenue streams to the registrar. Why not take that margin and recurring revenue for yourself? Its not like its hard nowadays to set up as a reseller - getting accredited is slightly more complicated, but it you can make it as a reseller, then even that hurdle becomes pretty achievable.
a) build it so that you can license the technology to people that have made a company out of selling domains (domainsbot.com is a great model to take a look at)
b) become a reseller or registrar so that you can fully deliver the service and collect the recurring revenue.
There's still lots of room for innovation in this space and I think you are leaving a lot on the table if you don't flesh out the business model a bit more.
(obDisclaimer: I work for a registrar.)