Local playback is fine, but greatly restricts your options for media boxes. The top end Apple TV 4K for example only has 64GB of storage, and the Nvidia Shield TV caps out at a paltry 16GB. The Apple TV would fit a few shows if you were willing to rotate them out, but wouldn’t be able to provide a “library” experience. The Shield supports external storage, but who wants an external HD or NAS taking up space on their TV stand?
So local playback implies something more like a mini-ITX PC or SBC running some flavor of Linux. That’s fine, but it’s not going to be terribly couch-friendly since it’s going to have a bog standard desktop UI.
So the most popular option is to put all your media on a server in the closet (usually an old laptop or raspi or something), with a client on your streaming box like Plex, Kodi, Infuse, etc connecting to your server.