> like 1mW with the size factor of a normal battery

It seems like Carbon-14 is just not very radioactive, and if I read the Wikipedia article right, Geiger counters can't even detect the radiation for small amounts, which makes me wonder if they would even trigger around the 1 gram in those batteries.

Looking at a bit more sources, Carbon-14 radiation has a maximum distance of 22 cm in air and 0.27 mm in body tissue. The half-distance layer in water is 0.05 mm. In addition, Carbon-14 in nuclear waste tend to also include tritium, which is even weaker.

If we wanted powerful batteries, low-level waste seems like a bad choice. If the material don't even need shielding to be around, it is unlikely to carry a lot of energy. Intermediate-level waste and high-level waste would likely be better suited, especially Intermediate-level waste since those do carry a lot of energy but does not require cooling.

Could be useful for things that wake up very infrequently and run for a short amount of time.

Nearly all of the devices you would want to power / we have the ability to build have a lifespan orders of magnitude shorter than the lifespan of the battery. It just doesn't make sense any way you look at it. The top comment is right. There's much better, more cost effective solutions for powering the proposed device, and better, more practical uses for the 'spent' nuclear fuel.

Pacemaker?

The pacemaker is probably only designed to last for 50 or so years. I'm not an expert, looking up the statistics, that seeems to be a very generous estimation. So you want to put a power source that can last hundreds of thousands of years in a device that's going to last 50, at great expense?

Well, there aren't many reliable chemical battery designs that can last for a few decades. We have stuff that lasts for at most one decade or two, and we have the nuclear stuff.

Of course, if you are using the nuclear stuff, you will prefer something shorter lived, so you can use a smaller battery. But I don't see why that huge objection on using the longer lived stuff too.

After death, the person will be giving back his/hers "water of life", like in Dune, to be reused by others :)

What could possibly go wrong?