I didn't even know this was a thing, selling off the servicing of loans. Our first home's mortgage was with HSBC and HSBC did everything, up until we sold that house. Our second (now current) home mortgage was with a local credit union and they did everything, too.
Dealing with the local credit union was super easy for everything. Not that HSBC was bad, but the credit union was always local people to talk to and never any problems.