You could open source it anyway, though, or parts of it. NewsBlur does this: https://github.com/samuelclay/NewsBlur

One could run their own NewsBlur, but Samuel has stated it requires a lot of resources to pull RSS feeds, and so in practice it's much easier to pay them $2/month. (This may not apply if you plan on having business customers who are paying orders of magnitude more than that.) But it alleviates any fear that the service users depend on may disappear; in the worst case, run it yourself.