This is a huge piece of it, stop ripping us off! This has been going on for decades -- from NiMH battery packs for power tools, to laptop batteries.
I assume a big difference in the danger aspect with the bike batteries is their size/capacity? Less to go wrong with a 2AH cordless drill battery, than a 20AH bike battery?
But a 50 cell 36V 625Wh e-bike battery is an entirely different beast and when it goes you're going to be very sorry if you are nearby. Individual cells that go are already very impressive, a large pack is going to very effectively spoil your day (if not your life).
625 Wh is the energy equivalent of a few ounces of gasoline. That's certainly enough to do some damage, especially if it gets misted to an explosive air/fuel ratio, but not something that most people would be afraid to handle.
What will happen - usually - is this: one cell will go bad, into thermal runaway. Maybe it had a bad interconnect which vibration fixed and now the rest of the cells in parallel will dump a few hundred amps into it or maybe the pack was subject to a fall, who knows. But let's assume that one cell only got damaged. This cell is in close proximity to the rest of the cells in the pack but typically they'll have between two and six closely spaced neighbors. Those in turn will start to go up after which there is a geometric expansion until the whole pack is gassing out and possibly already burning.
Elapsed time from first symptoms to violent explosion/fire is on the order of 10 to 20 seconds at best. And once it gets going your best chance of stopping it is to immerse the whole thing in a very large volume of water or to bury it in a large amount of sand. The vapors are not going to be pleasant to deal with, anything combustible that it can come into contact with will likely burn.
Some examples:
Even the big manufacturers mess up. That's a pretty good sign that this isn't an easy problem.
There are things such as space heaters, heating pads, kitchen appliances, etc. that have been known to start fires, but at least if you're in the room with them you can probably react and extinguish them if you have water or a fire extinguisher handy.
The big thing that stands out for me is that the perception of the risks (impact / likelihood) is entirely unlike the real risk. For most other things those are much more in line. And that's why people get caught out.
Nobody thinks twice about leaving their e-bike charging in the kitchen overnight, or to take it into an elevator or in an extreme case even a bedroom (1 room studio, no storage space). Stairwells are another such spot. I charge mine outside under an overhang, and only do so when I know it isn't going to be anywhere near freezing.