You meant infinite charcoal, not coal, and you don't even need to mine any coal to start with.
While they seem the same and are even the same item with a different data value there are some differences; try trading charcoal for emeralds (unless you are in 1.7.10 or earlier); you also can't make blocks of charcoal (though it would have been very easy for Mojang to add).
Also, you can truly get infinite coal with a Wither skeleton farm, although I personally think that it is pointless to farm coal/charcoal except when you first start out and need to make torches since coal ore is so common (in my current world I've mined more than 2,000 per day for over 100 days... even one hour has given me more than I've needed for any use unrelated to caving).
At first my reaction was "well, this works, it's infinite (char)coal from one", but then I realized the obvious wood consumption. To be fair the title never said it was free, but I need way more wood than coal, as I play primarily by building and coal really only gets used for torches (granted I need a lot), whereas wood is needed probably way more than anything else (I deforested many entire areas in developing the places around my world). I'd say cobblestone gets used a lot too, and it does, but I have way more of that in storage than anything so it's probably wood. So, I can't really afford to waste wood for torches or smelting, and using coal gives me an excuse to mine and go caving too to break it up from being nonstop building (it creates adventure too, as sometimes I literally wander to various parts of my world for a cave even if there's some nearby, which has the added benefit of me going "oh this area is nice" and there you go, new planned development location for later).