Kodi does have bultin server functionality (both DNLA and a web interface), it's just less commonly used that way, and I don't think transcoding is supported without plugins.
Kodi is 99% a TV-like frontend to a local-disk media collection, its web interface is an afterthought, its performance for remotely served media is atrocious.
Jellyfin, Emby and Plex are media servers first and foremost.