You may not realize that there are really 4 different kinds of shippers that e-commerce retailers may offer to their customers:
1) "Integrated" shippers: FedEx, UPS, (DHL, though not in the US anymore)
2) "Mail": USPS
3) "Hybrid": UPS Mail Innovations, MailExpress (you mention both, but they are actually competing services)
4) "Common Ground Carrier"
An integrated shipper has its own ground fleet that does a combination of picking up and dropping off individually-identified packages on a route, going to a hub to exchange the things it has picked up for the things that need to be dropped off a certain number of times a day. They have a separate air/ground linehaul fleet to transport things between hubs, using the air fleet exclusively for next-day services, and using linehaul for heavy/cheaper 3-5 day services.
The US mail is a bit more complicated - as it runs a 3-tier system that handles a 'flow' which doesn't actually keep track of individual packages, unless they are on an overnight or registered service - so you have no real idea where it is within the 3 tiers of sortation/forwarding until it arrives, and if it somehow gets lost or stolen by Cliff Claven somewhere along the way, you will never know.
A hybrid carrier is lower cost than the integrated shipper, by taking advantage of the best part of the USPS - the fact that they have a vehicle coming to your house every day anyway. They pick up large volumes of shipments from the retailer, take it to a regional hub, and give each a unique ID, validate its addressing, weigh it, etc., just as Fed-Ex or UPS would. They then sort it and figure out what destination hub it should go to, and put it in with all the other packages going to that hub from the originating hub, again just like an integrated carrier. They then put those containers on either a commercial airline cargo service or a third-party trucking service, which they have an agreed service level from one hub to the next. They ensure it arrives at the hub on time, since they are able to see both the pickup and the delivery. They then re-sort it into which post office route each package delivery address is on, and deliver these bundles to the local USPS office, where the existing postal route driver picks it up along with all the other deliveries for his route. You get the same traceability as an integrated carrier for less than half the cost (because the delivery fleet is most of UPS/FedEx costs).
A common ground carrier is usually a trucking company that is arranged by the seller to take something point-to-point. You usually have no way to keep track of it other than through the seller, because they are the one with the contract with the carrier. This is usually really expensive, but your only choice for really big, really heavy, or hazardous material shipments.
4 days is not unusual for any ground service from KY to AZ. If you wanted it next day, either pick it up in-store or specify overnight air service from FedEx or UPS (and you will pay alot for it). If you want it in 3-4 days for alot less of a delivery charge, use UPS Mail Innovations, or MailExpress (though if it is heavier than 5lb, the USPS can't carry it on their delivery route, and you will have to pay for UPS Ground or FedEx Ground).
If you bought something with 'free shipping' - you are of course going to be at the mercy of the retailer to decide how to get it to you for the lowest cost to them
Shipping is one thing where you tend to get what you pay for.
