I think the 'burning e-bike problem' on the few occasions it occurs are to do with e-bike conversions, most likely as a result of buying a pick'n'mix of motors, chargers, batteries, controllers etc many of which are available online. Bafang do various of the 'reputable' ones - I know someone who used one to convert his bike - but some others are too cheap!
The battery for my bike has been charged, as required, without me standing over it for the past 5ish years but then it's a named (Fazua) system using the original charger.
The Lithium (LiFePo4) battery that's been fitted to our caravan for the past year also doesn't lead me to anxiety because, again, it's a reputable make and technology (KS Energy) with a lot of information available on their website, especially in respect of the Battery Monitoring System, and compatibility with car, caravan and solar chargers.