I visited a lighting store in town that sells dozens of front porch lights. None of them have an integrated GFCI outlet, which would be handy for my situation. The sales manager said that such an outlet is not to code and so they don't carry any such lights.
But I see them for sale elsewhere, including by major brands. For instance, a Hampton Bay item at Home Depot: "Mission Style Black with Bronze Highlight Outdoor Wall Lantern with Built-In Electrical Outlet (GFCI) Model #30264" has two integrated GFCI outlets and is UL-certified.
I see why GFCI protection is essential given that the plugged-in load could be exposed to water or fail in a dangerous way. With that in mind, is it to code for a porch light mounted on a wall to have integrated GFCI outlets? In case it matters, this fixture is about a foot below a porch roof and two feet inside the side edge of such roof, so it will not be exposed to direct rainfall.