There are people on YouTube who have created nuclear batteries by using a tritium source. They produced power, but in negligible amounts. There is a theoretical maximum amount of energy you can get from an emitter and for something that isn't very radioactive it isn't much.

They talk about energy density as well, which is a bit of a misnomer. A solar panel weighing 10kg can produce 8kwh every day for 25 years so it's better than gasoline or diesel, but you don't want to drive your car 25 years from now, you want to drive it today. Likewise, you don't want to drive your car 5000 years from now, you want to drive it today.

Judging from the source of carbon 14 you'd also quickly come to another issue, that even if you took everything at face value and these are the best batteries on the planet and they'll cure 120 illnesses and they make Julianne fries, there's a limited number of graphite moderated nuclear reactors, so the materials for building these batteries is really limited. You'd be taking a very finite resource and refining it so there's an even smaller amount, I suspect that a battery that could run a phone would cost more than a car, and a car running on a carbon battery would be the only thing running on such batteries that decade.