The short answer is no: a broken leg is not automatically a total loss. In my experience, most outdoor benches with a broken leg can be repaired well enough to be safe and solid again, especially if the break is in the wood rather than a badly rusted or cracked metal frame.
Start by looking at the break. If it is a clean split or snap in one wooden leg, you have several good options. Clean the broken ends, apply a high-quality exterior wood glue, and then reinforce the joint with long exterior-rated screws or a metal repair bracket. For best results, clamp the pieces tightly while the glue dries, then add the screws or bracket once the glue has set. This creates a stronger repair than glue alone.
If the leg is too splintered or partially rotted, don't try to glue it back together. Cut away the damaged section or remove the entire leg, then replace it with a new piece of weather-resistant wood such as cedar, teak, or pressure-treated lumber. Match the size and angle as closely as possible, then attach the new leg with exterior screws and, if possible, a corner brace or metal bracket inside the bench frame for extra stability.
Metal benches are a little different. A cracked weld or snapped aluminum leg can sometimes be repaired by a professional welder, but this may cost more than the bench is worth unless it is a high-quality or sentimental piece. For lightweight aluminum or tubular steel benches, replacement parts are sometimes available from the manufacturer, but many budget benches are not built to be repaired easily.
Before you put any repaired bench back into use, check the other legs and the frame for hidden damage, rot, loose joints, or rust. A repair is only worth doing if the rest of the bench is still structurally sound. If the seat, back, and other legs are badly deteriorated, you may be throwing money and time into a losing project.
So when is it a total loss? If the frame is severely rusted through, multiple joints are failing, or the wood is soft and rotten in several places, replacement is usually the smarter choice. But a single broken leg on an otherwise solid bench is almost always repairable, and with the right materials it can last for many more seasons outdoors.