It's exactly how Plex works (and how I use it). There's a server you install on your main computer (which is free), and clients for various platforms. It's the same basic thing as DLNA, and the server even works with DLNA clients, but the interface is much better if you use Plex clients or the web browser version.
You don't have to go through the browser, it's just an option that happens to be free if you want to try it. The native app is in pretty good shape already, but it still has some buffering issues; sadly Plex is stuck using the codecs Sony gives them.
The Plex UI is pretty sweet, it does indexing like XBMC so if you use a Plex client it's like you're using Netflix, the server keeps track of what you've watched, shows cover art, and has video descriptions.
https://plex.tv/
I'll probably do an official thread once the PS4 app is out of beta (assuming I can put it on the gaming side) so that people realize it's a thing. If you're really interested, it's $5 a month while it's in beta, or free if you just want to try the browser (the browser client has issues on PS4, be warned).