I've definitely designed in a through hole horizontal-mount USB-C port, where all the data and power pins are THT, but certainly does make the routing quite difficult! The drill holes end up being pretty small.
But would you expect a real stability benefit from using THT for the data and power pins? Those tiny wires won't help much in bearing any mechanical load. Solid through-hole mounting tabs should be fine to hold the connector in place and resist any torque from the plug; the actual contacts can all be SMD.
Based on repairs I've made in the past to devices using USB Micro B, I don't rate just having through hole mounting points as being sufficient. The typical failure point is that the connector remains rigidly mounted to the board, but the SMD pads flex up due to cyclic load. It is true that it is better than SMT pads alone for mounting it, and that repairs are usually easier because only one or two tend to break rather than the whole lot, but it's still not ideal.
At a guess, the failure mechanism would be due to the inner plastic moulding allowing just enough movement of the pins to create a fracture point at the interface between the PCB and connector. This flex is necessary to provide the mating tolerance and spring force on the pins, but the force is unfortunately transferred into the fragile pads.
I haven't yet seen enough USB C devices to say if their SMT connectors are better, so it might be unnecessary for USB C but I would prefer to use THT myself until it's shown to be unnecessary. The fact that they are offered as a product suggests that there is some demand for improved reliability here (I can't imagine there are that many USB C products where THT would be necessary for other reasons, like an inability to use SMT parts.)