You can keep the fixture, the glass, the warm old glow, and still cut the heat and the power bill. A period-correct vintage LED bulb lets a fixture keep what you see while changing the one part worth changing: the bulb.
Heat is the weak link
The problem LED solves is real. Old fixtures were built for incandescent bulbs, which run hot, draw heavily, and, in some sizes, have grown scarce. Heat is the enemy of an old fixture, cooking wiring, cracking glass, shortening the life of everything around it. Incandescent bulbs throw a lot of it, and high-wattage sizes like the mogul are also harder to find and expensive to run. So the bulb is the weak link, not the fixture.
The key phrase is period-correct. A generic LED with the wrong color or a harsh cast will wreck the look of a vintage fixture no matter how good the glass is. What you want is an LED that matches the warm color of old incandescent light, sits in the right base, and, where the bulb shows, carries a filament-style look. Behind an opal or frosted shade, a good warm LED is indistinguishable from the incandescent it replaces. The gains run one direction: less heat, less draw, longer life, same light.
Salvager's Note: For a vintage fixture, choose a warm LED (about 2400–2700K) in the correct base, and a filament-style bulb wherever the bulb is visible. A cool or bright-white LED will give away an otherwise perfect restoration in an instant.