I use a lot of Li batteries and know all too well the need for proper care and attention to charging them. Always charging when you’re there, and not overnight when you’re asleep, hoping the charger circuitry will cut off as designed is putting your trust in a less than $0.10 balanced charging chip is a setup for a granted rare, but devastating m, outcome if that fails. Always charging on a nonflammable surface is also the right way to do it.
To stop smoking I took up vaping about 5 years ago. Despite all the gum, patches, meds, hypnosis, nothing stopped my pack and a half day habit. This did. That’s not to say it’s for everyone, certainly not a non smoker, but for those who need to stop it does work as a harm reduction strategy. I use a lot of high current 20-30A Li batteries which are safe when treated with respect. I also have some devices with Lipo packs, similar chemistry but in a soft compliant case to adapt to unusual spaces where a plain cylinder won’t work. You also see them used for RC cars and drones. They represent their own challenges in safe care and feeding. So your point about not treating any large Li battery with anything other than safety first is right on target.
As for situations where say a Fitbit might not charge, it may be that the draw is below the typical 500 mA that a usb plug was created for (laptops and PCs). It’s possible power brick circuitry may view a draw below that as out of spec, and cut the current as a safety step. I don’t think I’ve ever run into that, but it is a possibility.
The other thing to remember is even if a charger/brick is designed to deliver up to 2-3A on it’s usb plug, it’s the device plugged into it that determines the current draw. Plugging an item in that can only use 500 mA to charge is safe, as it’s running the show (assuming it’s functioning properly). The charger/brick battery does not push electricity into the device, the device establishes the draw. But if you plug in something that can draw up to say 2A for rapid charging (phone, tablet, whatever) into a transformer rated to deliver only 500 mA to 1A will get a bit warm, and if cheaply made, overheat(think of those $0.99 wall warts you can pick up at 7 Eleven or a gas station, they can overheat, fail, and even start a little electrical fire and melt the plastic transformer). It’s the same reason using your laptop USB port which is rated at 500mA to charge your phone or tablet isn’t a great idea. It can overheat the port, and shorten the life of the port.
TLDR, but the bottom line is follow the instructions on charging any device, and use quality transformers and portable battery chargers to meet your needs. The instructions that come with the devices really are there to keep you safe.