This is a settled matter in Code.
There already is a practical case which illustrates your question.

In 1966, when they finally put their foot down and grounded everything, range and dryer manufacturers asked for an exception to allow ungrounded 3-wire circuits (hot, hot, neutral) to continue to be installed. They said "We can ground the dryers and ranges to the neutral wire. And, that shouldn't be a problem because dryer and range receptacles are rarely ever disturbed". The exception was granted.
Thus, they gave your concept the Pepsi Challenge. They really did. For 30 years.
Now, the NFPA is a data-driven organization. They like hard numbers and accident reports. So in those 30 years they were not idle, they were collecting data, "seeing what happened".
And then in 1996, having gotten their answer, they outlawed the practice.
Feel free to delve into the record of the NEC code-making committee's discussion in 1996 as to why they changed it after 30 years. Or read the Handbook, which discusses the rationale behind many rules. (thanks Ed Beal for the suggestion).
I presume their reasons related to the body count!
Your thoughts
But why not "ground" the chassis to Neutral? Wouldn't that do the same thing? Ground and neutral are even tied together, at the electrical panel.
"At the main service panel" is not the same thing as "NOT at the main service panel". That's what you don't understand. It's because you are laying down a huge presumption that wires just get from one place to another magically, and this doesn't involve any actual stuff that could break.
Giving a look at the post, it looks like ground is there just to act as a back-up neutral. Is that really all there is to it?
"A back-up neutral so the light stays on when the neutral breaks" is a dramatic misreading of that post. The scenario where the neutral fails, and the service current re-routes through ground, is the BAD case. Look carefully, and you'll see it sets up a tragedy in the next slide, when ground also fails.
Indeed, this is the nut of why 3-wire dryer and range connections were banned.
Ground is absolutely not a backup service neutral. The desired thing, when neutral breaks alone, is for the device to stop working. That will motivate people to fix it properly.
Keep in mind also, on 35A or larger circuits, the ground wire is smaller than the neutral, and simply cannot do the neutral's job.
I guess it makes sense - a break in Hot, you're fine. A break in ground, still fine. A break in Neutral, you need a backup (the ground)... so basically adding a second layer of protection to the only wire which needs it?
One of the most dangerous things is a "sleeping menace" condition where there is a dire hazard, but it is not actually presenting as a problem. So to follow your comment:
- A break in "hot" shuts down the appliance, so the person knows there's a broken appliance or circuit, resulting in immediate repair of the circuit and thus, no sleeping menace.
- A break in "neutral" also shuts down the appliance, also resulting in immediate repair of the circuit and thus, no sleeping menace. But a break in neutral does not degrade the grounding protection so if the same casualty causes hot to get loose, it will still trip the breaker. And by the way, breaks in neutral are very common. We get "head scratcher" tier problems all the time that trace back to a disconnected or degraded neutral, and Lost Neutral is the most common whole-house failure.
- A break in "ground" removes a layer of protection. Understand the system uses "defense in depth" or the "swiss cheese" model, there are several layers and all must fail in a particular way (the holes in the swiss cheese must line up) for there to be an accident. So it's not good, but a break in ground doesn't immediately cause an accident. This is the only one that "fails silently" creating the sleeping menace.