The post office does things that private carriers are unable to do: deliver a high volume of units to any valid address. FedEx pushes a fraction of the volume of USPS and is buckling under the strain of the current labor shortage[1]
FedEx is so bad now that I avoid buying from sellers that use FedEx for shipping. The last few times I had a FedEx delivery, the delivery status went to pending twice, and the deliveries were a week late. Looking at the Google Maps reviews of the distribution centers where the packages sat, I consider myself lucky to have received the packages at all.
The Post Office doesn't actually deliver to every address. There are hundreds of rural areas where residents get a free PO Box in the nearest town, without the option of home delivery.