The collection of GST is a real dog's breakfast! Amazon and ebay rolled over and agreed to collect it (and forward it to the ATO, although how the ATO know it's all been sent I don't know). The big surprise is Aliexpress agreeing to collect it. I'm sure that they will forward all of it to the ATO.
I'm not aware of any other US companies who are acting as tax collectors for the ATO (I can't see why they would want to), they generally say that local taxes are the responsibility of the purchaser, and therein lies the problem for the government. Given the huge amount of parcel traffic coming into the country it's not feasible for any department to stop and check every item and then notify the recipient that GST is owing thus the move asking overseas companies to act as Australian tax collectors.
Don't forget, too, that this whole mess came about because Harvey Norman wanted a "level playing field" so pressured the government to stuff up what was a perfectly good system.