Not sure if MC sugar cane is burnable, either, but paper is made from plant fibers and plants are flammable (forest fires aren't powered by buffalo chips or cow pies, ya know!). Because sugar cane is a plant, it would be flammable and therefore paper would be flammable as well. Ergo, to maintain internal world consistency paper should burn or at least have some sort of fire-starting property.
I don't think paper should be fuel for redundancy sake. There's already an abundance of fuel sources in Minecraft, and wooden planks, charcoal and coal are such efficient fuel sources that there's no need for a new fuel source. Paper seems like it's supposed to be a mid to late-game item based off of its use in fireworks, enchanting tables, bookshelves and trading for emeralds. Sugar cane itself can be composted and turned into bonemeal, so adding a fuel recipe to paper seems redundant as both paper and its base plant serve a variety of purposes.
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Watch out for the crabocalypse. Some say the day will never come. But it will.
Feel free to drop by for a chat whenever.
If you'd like to talk with me about other games, here are a few I play.
Team Fortress 2
Borderlands series (Borderlands 2 is my favorite game, ever. TPS combat is a lot of fun and makes up for the lower-quality story, in my opinion)
Elder Scrolls series
Warframe (IGN is something like That_One_Flesh_Atronach)
Pokémon series (HGSS forever)
Left 4 Dead 2 (Boomer files always corrupt though)
SUPERHOT (SUPERHOT is the most innovative shooter I've played in years!)
Dead Rising series (Dead Rising 2 is one of my favorite games, and the 3rd was a lot of fun. 1st has poor survivor AI and the 4th is bad)
7 Days to Die
Just Cause series
Come to think of it, I mainly play fighting-based games.
As someone who has made campfires IRL before, you would definitely not be able to cook, much less smelt, using paper as fuel. A piece of paper takes about 2-30 seconds to burn fully, depending on how much fuel you are already burning in a fire and how big the piece of paper is. If the paper burns quickly enough, it will make the fire burn bright for a very, very brief moment, and then the paper will turn into ash.
At most, you would only use paper to fuel a fire since it's easy to get one started this way. However, you need wood or coal to burn in order to produce a fire that produces enough heat to cook food or smelt metal. (Heck, the latter shouldn't even be possible with wood. Iron is usually smelted in Bloomeries, where charcoal and iron are put in an incredibly confined area to heat it up to incredibly high temperatures.)
I get offtopic a lot, be warned. I also often mention a Minecraft clone called Minetest. The clone is nowhere near playable with it's default game in my opinion, but it's at least the start of a good open-source voxel rendering engine, and maybe one day it might be decently playable.