If you can fry an egg on a car hood that’s been out in the sun, I’m pretty sure you can cook stuff on glowing hot embers.
Flames are just a biproduct of fuel molecules being ejected into the air and decomposing, which in turn gives off light. (to put it simply) Just because something is not giving off flames doesn’t mean it’s not hot. Magma doesn’t give off flames. It is still molten rock, however.
I don’t know how many things I have cooked over red hot coals just like the ones in that picture. I don’t know how many times I have tucked a piece of wood into coals like that and watched it immediately burst into flames. So I don’t know why you think it can’t cook stuff. =P
Anyway, I like the idea. Fuel added to hot coals should have a chance to ignite automatically (perhaps some kind of flammability stat for object? I dunno) and thus you could keep a ‘campfire’ going without the need for additional matches. Just like you can in real life. Hot coals should turn to cool coals just for effect, which can disappear over time like blood stains.
Also like the idea of making charcoal. You should also be able to build a charcoal pit by digging a pit, and then building a charcoal pit from the menu (survival?) using chopped wood and a shovel and an ignition item. Then you wait 24 hours and bam, stacks of charcoal. Which make for good fuel sources and might be required in other recipes.