That sounds pretty typical, didn't know they used to not charge for a residential pickup.
To be fair businesses that have a FedEx / UPS account and have regularly scheduled pickups do get charged for that. It's one of the items buried in the bills you get from them every week (can't remember offhand if the pickup fee is a weekly or monthly charge). Maybe the high volume businesses get it for free, not too sure.
I'd expect USPS to do the same but don't have any direct experience with their billing.
Where I work we have a similar situation, we sometimes have prepaid FedEx labels but no regular FedEx pickup so that has to be arranged differently on our end. We could pay FedEx their pickup fee if we wanted but we don't ship FedEx every day so it's kind of a waste of money, and the FedEx drivers would be coming and going without picking anything up most days.
Well yeah, USPS should be cheaper. They tend to get bailout money from the U.S. government due to operating at a loss e.g. https://www.reuters.com/world/us/us-senate-approves-50-billion-postal-service-relief-bill-2022-03-08 , UPS/FedEx on the other hand just raise their rates / change services to keep their shareholders happy.
In theory if the USPS was allowed to increase rates as much as any private company then they would be as expensive, if not more, vs UPS/FedEx.