Me too! Never heard of lasership. Is UPS too busy that Apple is resorting to using other shippers???
LaserShip and companies like it, such as OnTrac, are typically used for expedited shipping. My same-day Amazon Prime orders are almost always delivered through one of these services, as well as my Blue Apron food like someone mentioned earlier.
Having one of these couriers ship your product doesn't typically mean the big two (FedEx, UPS) are too busy to handle the orders. It usually means you're going to get the delivery really fast, in 0-2 days.
My guess is the big two will get the product from China, then to US distribution, then to state distribution, then sub it out to these "last mile" couriers. It's probably more cost effective sending it to them, whose only job is to make deliveries a small region.
My band went from "preparing for shipment" last night, shipped today (OnTrac), and will get here tomorrow. AKA 1-day shipping. This seems to be the case with everyone's order I've seen so far