Lycoming says it's ok and it works very well.
I take a different meaning from the same Lycoming instruction;
Priming can be best accomplished with an engine priming system, as opposed to use of the throttle.
And goes on to [correctly] advise about engine fires resulting from excessive "throttle" priming. And, it's worth noting that where there is a conflict between the engine manufacturer's published information, and the airframe manufacturer's flight manual, the flight manual shall prevail. Lycoming has no design control over the airplane manufacturer installing a hand primer as a part of the type design, so something is better than nothing, but they are saying that a primer is the best way to prime. The POH's for a Lycoming powered 172 and 177 do not mention using the throttle to prime at all, though give instruction to use the primer.
It is possible that a Lycoming engine could be installed in an approved airplane type, for which there were no dedicated primer system, and then, yes, throttle priming would be better than ruining a starter motor trying to start an unprimed engine, but the fire risk would still be there. That'd probably be why every Lycoming carburetted engine I've ever flown has a dedicated priming system.