(Former UL engineer here, worked there for 21 years and part of that on battery chargers and lithium power tools. (electronics engineering background) Now I work for a tool company that builds lithium power tools and I'm the regulatory engineer for them.)
UL Listing on battery packs and chargers would mitigate almost all fire concerns. Yes, there are a lot of tests that the products would have to pass: both normal and abnormal. (forseeable misuse) Manuals probably say to not charge unattended, but that is unrealistic. No one (or very few people, anyway!) is going to sit there and watch their bike or battery charge for 4-8 hours.
A UL Listed battery pack would have to use certified cells, which have CIDs built-in. (Current Interrupt Device) If the current gets to fault levels, this CID would pop and open the cell. Then, the BMS (battery management system) would be tested. Ideally it would be tested in combinations: battery+bike and battery+charger. There would be component faults in the BMS. With the charger, a cell imbalance is introduced by discharging one cell or parallel cluster of cells, then putting them back into the battery circuit, then charging the pack. Since chargers usually only measure the whole pack voltage, this is a tough test, because it means the rest of the cells in the pack would be overcharged for the pack to get to the cut-out voltage. There is the shorted cell test, too. Of course shorting the discharge contacts of the pack is a forseeable misuse, and also overloading of the charger, due to a faulty or tired battery pack.
As for temperatures, a warm charger is nothing to worry about. The external temperatures are only limited to the extent that they shouldn't burn a person putting his hand on it. However, remember that if the charger is 50°C (122°F) externally, how hot is the transformer inside? How about the PCB that supports the current-carrying traces. It's a LOT hotter inside. UL measures internal temperatures, usually 15-30 locations to make sure everything is running within limits for each component. Electrolytic capacitors sometimes have pretty low temperature limits. PCBs are usually rated at least 105°C.
After testing the battery & charger, UL will control the safety-critical elements of the construction, so that the manufacturer cannot just change parts because they found something cheaper. UL then conducts un-announced inspections quarterly to make sure the manufacturers are still building the UL Marked products in the same way, year after year. The whole process is onerous and expensive, but this oversight is often needed to keep people safe. Remember when unregulated "hoverboards" were burning houses down? The government asked UL to write a standard for them and then required that incoming hoverboards were UL Listed. It's only a matter of time before the same happens for eBikes. Some manufacturers are already doing this voluntarily, having already been bitten in a few lawsuits.
I wrote this all out to point out that UL Listing can often be correlated with a certain level of quality. It's not causal, but I think you get the idea. Someone could still build a PoS product that is UL Listed, but at least it would be a safe PoS, hehehe. It's one of those things that doesn't matter until it's wanted, like a seatbelt.
I just ordered a multi-voltage charger from aliexpress. As far as I can tell, it's not UL Listed, but I'll have to wait and see which regulatory marks are on it. CE (for Europe) is self-declared by the manufacturer, so that doesn't mean anything on its own. It is just the manufacturer declaring he did the right thing. If asked by an inspector or government, he has to prove it, or else there's a big financial penalty. I'm gonna have to keep an eye on it. (I bought it so I could use it to charge a 48 V pack to a lower voltage, so that it is only really about 80% charged)
One thing I've noticed can be a fire hazard that is not often thought about are high impedance connections. An everyday example: Feel with your hand the temperature of the plug/cord junction on your toaster. Those often run hotter than they should. The impedance of the connection is too high, due to cheap spot welds, and power is lost there, turned into heat. If they're running warm, I cut those plugs off and fit a (UL Listed) mechanical clamping type plug from Home Depot. Notice how much cooler the plug/cord area runs after that. The same thing can happen with eBike charging connections. It's a decent amount of power being transferred there. On my heybike Ranger, it had a metal four pin barrel/sleeve connector, but he sleeves loosened up after a couple of charges and it was always warm there afterwards. I didn't like that at all. The two contact concentric connectors are usually better, in that regard, but they're getting to their power limit when charged at 60 V and 3 or more amps. UL has temperature limits on the plug prongs during their testing, but I suspect many products barely pass. Add a bit of manufacturing tolerance and ...