Competition in the overseas marketplace game have prompted them to step up.
Cheap postal service methods used to be the mainstay, with 2-4 week delivery times, or longer. And that was the good/fast method.
Now, when the nature of the item allows, they use private international couriers (like Yanwen, or Cainiao, owned by Alibaba), and rely on UniUni and others to do the last mile delivery. USPS still handles some as well, like for Yanwen, which doesn't have local arrangements.
A week or two is about average using those methods now. Denoted "Choice" items are warehoused in AX's own logistics system, and get shipped promptly, in bulk shipments for fast customs clearance, and can be quickly passed onto the local last mile courier. Multiple orders placed simultaneously can also get consolidated into a larger packages when the circumstances allow.
However, those private last mile couriers are a frequent source of compliant, and have poor reputations, but it's hard to say how much of the time they do fine. I've had a few such deliveries, and not had an issue, knock on wood. They'll also deliver on weekends, holidays, and such.
Going through China Post requires more sorting time in country, less frequent planeloads, and when it hits the USPS, each package has to individually go through customs, the ISC sort centers, before being shuttled off to the regional distribution centers, local distribution centers, and finally the local post office for delivery. Get thrown into the wrong bin and a package can take a circuitous sightseeing route.