Actually, a supernova would look like an impossibly tiny point source, much smaller than even your average laser pointer. I'm pretty sure the consequences of this haven't been thoroughly explored yet.
I'm not sure the Betelgeuse supernova, at a brightness around that of the full moon, would ignite fires, but I certainly wouldn't want to gaze at it with naked eyes, even at that brightness. IMHO such a light, given sufficient strength, could permanently damage the retina in your eyes.
I doubt it. Even without knowing exact surface power density that can cause damage to retina, the magnitudes discussed here sound far from dangerous.
You should know that even an impossibly tiny point source will get projected to a spot of finite size on the retina. The eye is not perfect - there is always some optical aberration. Plus, since we're talking about a star, there's also atmospheric distortion to think about.
The chances of light from Betelgeuse igniting a fire are very much zero. We're talking about light intensity about 10x lower than moonlight.
Your reasoning reminds me of the danger of retinal damage when observing a solar eclipse - a human's natural inclination to not stare at the sun is sharply reduced because the viewable area is so much smaller than usual. Looking at a thin slice of the sun is as dangerous as looking at the unobscured sun, even if it doesn't feel like it. But I don't think Betelgeuse would be dangerous in this way. It would be more like watching a lunar eclipse, which may be done without safety equipment.
I'm not sure the Betelgeuse supernova, at a brightness around that of the full moon, would ignite fires, but I certainly wouldn't want to gaze at it with naked eyes, even at that brightness. IMHO such a light, given sufficient strength, could permanently damage the retina in your eyes.