I would equate browsing for a movie to watch in a Jellyfin library (or Netflix, etc) on the TV to someone browsing at Blockbuster to find a movie to rent, seeing what is available on their DVR, or maybe even the TV Guide.

I think the media servers started as a way to avoid tapes/DVDs and making it easier to get content on the TV. It’s a much better experience than a 100 DVD changer. Now, it evolved based on anxiety around streaming services and never knowing when the TV show you’re watching will get pulled, or your favorite movie will lose availability… and wanting to maintain access. This is especially true as companies, like Sony, remove digital copies of movies people “bought”. So any digital file with DRM from a company is only good as long as they decide to keep offering it, which isn’t forever.