These ICs actually work extremely well and are designed to remain safe in case of a failure (e.g, blowing an irreversible fuse if a problem is detected).
Plus modern battery system designs usually incorporate secondary over-voltage protections, and then layer in software protections on top that (such as charging timeouts).
In fact I've never heard of a widespread battery issue due to complete protection system failure. Not saying it can't or has never happened, but that it would be quite rare.
There are however many cheap products built without any protection ICs, or with inadequate or counterfeit ICs, etc. Many cheap e-cigarretes and so called "hoverboards" fall into this category. I've even seen protection devices on boards that's not connected to anything -- designed to fool casual inspection by customs officials, etc.
But assuming proper design, battery failure is more likely to be caused by a manufacturing defect inside the battery itself, or due to a physical damage of some sort, or due to some sort of misuse.