Yes, there is a risk of failure involved with anything electrical, but I don't see why anyone would consider chaining extension cords inherently dangerous enough to ban. It increases the number of connections, but that's a miniscule risk compared to the 5+ connections an extension cord might have on its own. The only significant risk I know is people disregarding the max amperage rating of everything in that chain.
For anecdotal experience, I've had both extension cords and wall plugs fail (nothing serious thankfully, but they did get a bit melted), but in those cases it had nothing to do with my extension cord chains, but rather an internal connection failure.
AFAIk, the rationale for extension chords is that they are sized to cause a controlled amount of voltage drop within their lenght. If you keep adding them, you will increase the drop, and many devices will react by increasing the current.
This is correct. For a 120v 12FLA load at a distance of 50’, you’re fine using a #14 cord. If you double that to 100’, you need to use #10 cord to account for the voltage drop. As voltage drop increases, the amount of current flowing through the cord increases, which can potentially heat up the insulation beyond its rated temperature.
It is probably one of those little process changes to minimize chance of catastrophic failure. Sure, the risk of the daisy chained system going poof is low, but not zero. Instead, you should try to re-work your plans so you do not need to daisy chain.
For anecdotal experience, I've had both extension cords and wall plugs fail (nothing serious thankfully, but they did get a bit melted), but in those cases it had nothing to do with my extension cord chains, but rather an internal connection failure.