Hi JB (from another JB)
Not particularly. Semi-tame Red legged partridges are released into the environment in huge numbers annually to be shot at and plenty survive. They can turn up almost anywhere, even city streets, so a garden visit in the lowland south is quite a commonplace event. My in-laws used to see little groups of them trotting alongside their back fence which separated them from an edge of town school playing fields.
Artificially and unsustainably elevated populations of game birds and fish will attract natural predators. Nature invariably tries to correct an inbalance - Get over it.
They're not uncommon here at all. But I live in rural Northumberland in an area where there's a lot of hunting, shooting and fishing.
Very different sort of shooting and so they're actually not put out in huge numbers like pheasants though. We also have grey partidges.
A bird in the hand can make an awful mess!