I was thinking about it and we use charcoal, gas, wood chips, etc to heat our food; for obvious reasons and since they burn for a long time.  But what if, for example, you set a few steaks on fire and use those steaks to cook a hamburger? Would it improve the taste of the hamburger? 
It's possible to smoke meat using nuts or herbs, and fish can be baked on a huge slab of rock salt, but other than that, people don't really bother.   There's nothing wrong with experimenting though. Maybe you'll invent something new by burning fruit. Who knows.  