I used to not care that much about fire risks of cheap electric devices (apart from lithium batteries like here because they seem to be inherently volatile/dangerous) until one day few years back when a faulty wire of a $3 iPhone charger from AliExpress caught fire on my desk.
I probably wouldn't have noticed it until way too late if my cat hadn't happened to sleep next to it on the same table. He had a sudden scare of the fire and jumped quickly off the table. It looked so weird that I went and looked what he was afraid of and saw flames coming of the half-melted charger and the wire. The desk was full of paper and junk, it was seconds away from catching fire in a way that I probably couldn't put down anymore as I live in a flat and don't own a fire estinquisher. (We only have a fire blanket in the kitchen but that wouldn't have helped much.)
I will never save few bucks from charger wires or chargers or power banks like these ever again -- it's just not worth it!
That all said, don't have any experience from Anker devices myself but in my experience you typically get what you pay for when buying cheap.