You don't need to. But if you want to sync read state and favorites across devices, it's a good way. I self-host FreshRSS for this, works wonderfully.

Google Reader gives a good example of why one may want to host an RSS reader on their own.

1. Synced feeds, read/unread status, and consistent UI across all devices

2. Hosted feed reader for friends and family.

The author mentions the friction they imagine their friends or family would have using RSS feeds, so hosting the reader for them can reduce that friction and bootstrap cost (everyone already has a browser). Then they could always export their feeds and move to a different solution later.

This is an odd sentiment that I don’t have a counter argument for other than the beautiful UI of the app shown is worth hosting alone.