While largely forgotten by mainstream internet users, RSS feeds and RSS subscriptions are still supported to this day, and on Firefox there exist extensions like FeedBro and Livemarks to support RSS subscribing years after Firefox dumped native support.
The only problem with these extensions is that they offer no means to sync feeds across multiple devices through Firefox Sync. In the case of Livemarks (itself based on Firefox's old native implementation), the reason ultimately comes down to the way Bookmarks are tagged, as Livemarks saves RSS feeds as Bookmarks, but can only update those feeds when the original device is active (IE: the device the initial feeds subscription was made on). https://github.com/nt1m/livemarks/issues/22
I propose two solutions to this:
1. Update either Bookmarking tags or Extension Bookmark permissions to enable Livemark syncing across multiple devices
2. Implement a new native RSS Reader solution that could sync feeds across multiple devices (that is, one made with Firefox Sync in mind).
It is worth noting that nearly every modern web browser has some kind of "news feed" feature that allows for updated news articles on the new tab page. On Firefox currently, the equivalent is "Pocket" integration, wherein popular Pocket articles are shared on the new tab page. This could be incorporated into a native RSS reader, wherin Pocket is the default source but users are encouraged to subscribe to additional sources as they browse. Alternatively, Pocket itself could be reworked as both a "Read-It-Later" service and a RSS Reader, and could be a source of revenue for Firefox.
Update: With the news that Thunderbird will adopt K-9 Mail as it's Mobile Client with the potential to sync more than just emails between devices, Thunderbird's native RSS Reader could also be an opprotunity to sync RSS Feeds with a Mozilla Account.