When a player builds a fire or oven and stands very close to it for a prolonged period of time, the player actually starts BURNING. This is simply not possible in the real world.
The player should not start BURNING unless their body comes in contact with the flames. Cooking requires the player to not only be very close, but to MONITOR the food and the current system is just too risky to be worthwhile.
Stand in very close proximity to a fire for 5 minutes.
I just died from this while trying to cook my rabbit and cow steaks :(
I was healthy, hydrated and energized, I ran to a pond a few metres away and rolled around in the water, but still came very close to death. Then I went back to the fireplace and it happened again instantly even though I was drenched, and this time I died in less than two seconds.
The status messages ("my face is melting" etc.) are the only indication that you are on fire, so if you're not paying attention (e.g. because you're monitoring cooking meat) you could easily die without even knowing what happened. One might expect some screams and flames.
This was a fireplace in a stove in a house, if it makes any difference.
The above may also have been due to taking an extremely hot pot full of cooking food into my hands for several seconds.
I tried again, this time dragging the pot from the fireplace directly onto the ground when monitoring it, instead of into my hands, and avoided setting myself on fire this time.
But again, merely holding an extremely hot pot full of food should not cause your entire body to catch fire.