I have heard about batteries going into flames when left charging too long. And no doubt that can happen with a power supply that supplies just enough amps.
Is it possible for a battery to be badly designed such that it uses more amps than it needs? So, a power supply that can provide 2A to a device that needs 300mA, and the device mistakenly 'requests' all the amps it can get, and it gets all 2A. Or worse, the power supply can give 10A and it gets all that. And could it then ever go into flames from that? Is that possible?
So, if somebody has a cheap device like a cheap toy with a cheap battery in it, and they charge it from the mains..and the power supply can provide more amps than the thing needs. Are they more at risk if the toy or battery within the toy fails?
And if a supply can provide lots of amps like 10A, and a device only needs 1A, and there's a fault with the supply, is there more risk from a faulty supply rated at 10A?
Added- Assuming a good power supply, i.e. not faulty. And supplying a cheap faulty device. If the cheap device 'requests' more amps.. Could that happen? How likely is it? And in the event that it does, then would a good 1A supply be safer than a good 10A supply? Since, at least with the good 1A supply, the fuse would prevent 10A being supplied.