Something other than first past the post wouldn't actually change the outcome however. If I'm inclined to vote for the party most likely to win the election to avoid splitting the vote, I'm still putting them as my second choice and unless something really out of the field happens, my first choice still losses the instant runoff.

But the point is not to, necessarely, change the outcome of a particular election. The point is to allow people to vote by heart and, therefore, allow smaller parties to grow instead of die on birth.

No third party in the US has any chance at winning the current election, regardless of system.

I know. But that is not the point. Sure, Jil or whoever wouldn't be able to win. But that is fine. They would still receive votes. And more than they would otherwise. This mean they gain visibility so they can do better in a future election.

Furthermore, this mean two close candidate can run in parallel without ruining the other. Maybe Sanders would be able to run, confident he wouldn't destroy Hilary in the process.

A non FPTP would also mean a party can split without destroying itself. The saner part of the Republicans, for example, could just abandon Trump and his base and still be strong enough to compete in the future (a similar thing happened in my country recently).