First, I'd either do a deal with a registrar, become a registrar, or merge or partner with one. It's absolutely essential that the user own the domain that their feed is hosted at, so that, in case of emergency, they can switch to a different hosting service. If they don't own the domain, it doesn't matter how many promises the vendor makes, or how well-intentioned they are, an act of god could result in a blackout of a huge portion of the RSS network. It's irresponsible to host a large percentage of the net's RSS feeds at one domain. I would set it up so it's the other way around. My hosting service won't host your feed unless you own the domain.
Further, it would have to be very easy to set up, that's why we'd bake in the registrar functionality. We'd even suggest a domain name if you can't think of one, something like oe913qvijj.com or zeu5ba5wv.org.
The reason this works is that the domain name system has already been set up so that one registrar can take over the registration of a domain. No need to invent a new system. Your feed goes where ever you want, whenever you want.
Then, once you have a domain registered, you can check a box (which would be on, by default) that allows us to host your feed for you. Sorry, you will have to pay something like $7 a year for the hosting service, but you get to act like a customer, and we will treat you like one.
Further, I'd allow readers to become customers too. When they subscribe to one of the feeds we host, if they're willing to pay a flat fee, we'll eliminate the ads in the feeds we serve them, and share the revenue with the people who author the feeds. I don't really like ads myself, so I'd pay the fee, happily. Some people want to put ads in their feeds, and for them, we'd offer a competitive price, with the added advantage that we allow readers to not have to see the ads if they're willing to pay to not have to.
It's a little bit more complicated, but it's a sustainable business. When FeedBurner's users are up in arms when some media conglomerate has bought them out and is starting to redirect their feeds to Viacom and Fox properties, or inserting their own content alongside yours, like adding a idiotic liberal bedwetter post alongside your rant about immigration policy, or generally messing around with your ideas, we'll be above it, because you'll be able to opt out of our system any time you want. We won't be able to screw with you, because you'll be able to switch, easily, without our help. (If you've ever tried to get off AOL, you know why that's so important.)
Disclaimer: I'm not starting such a service, this is just to illustrate a point. But I likely would invest in a venture that was taking this approach.