Good luck finding any practical applications for a battery like this which only puts out a few microwatts or less power. Even with energy harvesting over time, you will not have enough power to run even a tiny, low power LED for long. Even if it output milliwatts of power, you'd still have a hard time finding any practical applications for it. This is why we don't see even the most low power devices using such battery technology. It just doesn't output enough usable energy and it doesn't scale well. Who cares how long it lasts if it can't practically be used for anything.
Yes, they are niche batteries for sure. Still an interesting technology and even more so from a DIY perspective.
Outside of scientific research, they really have no use even for DIY hobbyists. Dave Jones at EEVBlog covered these types of batteries in at least a couple of videos and showed how little power they are able to produce. He takes a practical approach with them and the verdict is quite bad for them.
Here's one of his videos on nuclear diamond batteries: https://www.youtube.com/watch?v=uzV_uzSTCTM
Ya, I've watched that before. As I said, very niche. But niche or not, remains interesting.
Btw, all of your points are mentioned in the linked video. He even measures the output.
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