The web player (currently in beta) is much better. I don't even use the desktop version anymore. I'd guess they gave up on the desktop client to focus on the web and mobile.
There is- the media keys work no matter what application you're currently focused on. A webapp couldn't do that, unless Chrome extensions allow you to do something weird.
And a web version is far more convenient than a desktop one- you can just load it up anywhere. Spotify's desktop app has slowly got slower and more resource-hungry.
I just use the mobile app when I am away from my own computer.