Are intersection takeoffs less common in the USA than in other countries?
US airlines are extremely fuel conscious. They have software that calculates the exact throttle and flap settings required for the exact length of runway available so that they don't burn any more fuel than necessary, and that is all typically computed before they even push back from the gate.

If the pilots know in advance (e g. from the ATIS) that intersection departures are in use, they'll calculate for that. However, if they're already taxiing out to the end and ATC asks if they can accept an intersection departure instead, they'll need time to rerun "the numbers" and reconfigure the aircraft. US ATC has learned from experience that this delay often negates whatever trick they were trying to pull off, so they usually don't bother asking unless there's a really good reason.

Also, unlike light planes, for safety reasons airliners are required to have enough runway available to accelerate to V1 (nearly rotation speed) and then brake to a stop again before the end if they need to abort. This means they'll rarely use more than about half the runway available. This is factored into "the numbers", of course, and is another reason why they need to be checked before accepting an intersection.

As to why intersections seem more common in Australia, perhaps there is some difference in how their airports are designed, or perhaps their ATC is just more willing to do it, or perhaps Qantas pilots are faster at running "the numbers" or have a habit of running all likely options instead of just the expected one.