Why isn't the alternative vote standard for most nations?
Voting is systems are, per the US Constitution, completely a matter for states to decide, not the federal government. As Article I Section 4 states:
The Times, Places and Manner of holding Elections for Senators and Representatives, shall be prescribed in each State by the Legislature thereof;
As such, the linked petition cannot be acted upon.
That said, the question then is: "Why don't the states adopt an alternative vote instead of a first-past the post?" There, you have a few factors, most of which boil down to incumbency.
Incumbents write the rules. They won on a first-past the post system, and there is thus no incentive to change it.
There is an implementation lag. If one state adopts it, but another doesn't, there could be adverse effects. A proportional voting scheme clearly hurts a state's influence, for example. Depending on the methodology employed, there could be issues.
In the US there are 2 major parties. These parties are run by people who are chosen by those people who donate heavily to the party and campaigns. Those people have a business(and monetary) interest in keeping the 2 parties that are currently dominant parties in control of the government.
If you look at the roles of those donors you notice something familiar. Many of the names are the same. That is because both of the parties are beholden to the same interests. They all talk a big game but when you look at the number of big campaign promises that are actually fulfilled as promised you can see a similar trend. The ones that are acted on are the ones that are to the benefit of the big donors. Similarly when you see an elected official renege on a promise it is most likely in the favor of the big donors.
So the answer to the question is, because neither the GOP nor the DNC wants it to change. Both parties thrive by having the other as the primary boogie man. Neither party as any interest in sharing that power with anyone else.