You are speculating that LEDs have zero internal resistance which is also incorrect. A Thousand hours is less than 2 months, so I can know about that soon.It is one of those myths that persist, treating LEDs as light bulbs. It is probably maxing out the power supply too, which is saving the LEDs for a little while longer. A component that is normally rated for many hundreds of thousands of hours is now down to a thousand hours or so, if you're lucky. It's not doing the power supply much good either, its lifespan is being affected. The heat is telling you something.
Most folks design for fail safe. When it finally goes out all the LEDs will have been damaged, not just the one that burned out. At that point fixing the design will come too late for those components, including the power supply. The damage is cumulative.