It would add even more clutter to fights. Imagine a team-fight going down in mid-lane where everyone is using their ults and abilities. Two people get popped by an adc/burst mage and suddenly you have two character models (potentially large ones) flying around while everyone else who's still alive is trying to focus. In the heat of the moment you might see a body flailing around (like a Hecarim that died mid-ult) and, not realizing that he was already dead, you throw your ult at him to stop him from getting to your backline. It would just add way too much visual clutter to an already particle-heavy game.
Also, a lot of champions already have unique death animations. Zed crawls into a little shadow portal, Brand burns up into a pile of ashes, Sejuani gets crushed by Bristles, etc. Ragdoll would make these impossible, so it'd be wasting a lot of work that people had already done.
Don't get me wrong, I think it'd be hilarious. Ragdoll is an awesome mechanic that has made many games way better just by existing. I just don't believe it fits into League's more serious dynamic. That said, it could possibly be used in something like URF, which is already over-the-top and meant to be pure enjoyable chaos.