1. Even though feeds are fairly small and easy to serve there’s got to come a point where you have so many users that even their small feeds begin to cost significant money. Feedburner not only has to check the host feed often but serve all the subscribers who poll as often as every 5 minutes. That’s a lot of bandwidth and a lot of server power.
2. With free analytics services all over the place it’s very unlikely you’ll be able to make money on a subscriber model which leaves ads as the only viable revenue stream. But for that to work you need a decent ad network behind you and you can’t very well use adsense
With that said, I'd think it a fairly easy service to duplicate. All Feedburner really does is read your feed and then repackage it while logging the pertinent data from the subscriber http transactions and sticking it in a database. Since every modern language I can think of has free libraries for reading RSS/Atom feeds and logging transaction data the whole thing could probably be duplicated in a couple days.
If not user specific: user requests feed for xyz.com: try to pull from cache. If there's a miss grab the feed from xyz.com, store to cache, and serve (be sure to set cache to expire in however often is necessary). If cache hit, you're done!
You can throw in extras, like make the cache semi fault tolerant by storing the latest feed to a DB. If your cache ever dies, then you can grab from DB to refill the cache.
Beyond that, it's just logging views and subscriptions to feeds.
Am I missing something? I don't actually use feedburner...
What are your options really? Either charge a monthly fee for a service that your users can find for free elsewhere (either right now, or eventually) or you can slide in ads between the feeds you serve that no one is going to bother to click on anyway.
The big appeal of FeedBurner for most people is their subscriber count monitoring and, unfortunately for them, it's something they don't do a very good job of tracking to begin with.
The other big unspoken aspect of FeedBurner is that those very counts are so easy to manipulate that trusting anyone's numbers is too big of a leap of faith anyway. The whole system is about bunk now.
EDIT:I say pick one field where Google sucks and improve it, make it better. One thing is for sure, you will have less competition by going against Google then by going against Twitter or FriendFeed or HN...
Looks like someone is launching a competitor: Feedsqueezer, http://www.feedsqueezer.com/
Well, it doesn't if you leave the feedburner account alive. But it would be great if google somehow allowed us to redirect the feedburner account elsewehere via a 301 redirect. Ofcourse, that will never happen.