This rule doesn't require an explanation. I have noticed that writers who use "suddenly" tend to exercise less control in the application of exclamation points.
First, I'll address "all hell broke loose." This is forbidden for a different reason than "suddenly." It's a cliche'. Martin Amis said that writing is a war on cliche'. It's heard writing. It's been said. The only time a cliche' is allowed is in dialogue, and even then it should be restricted. Maybe a character has a verbal tic where they always say a cliche'. Avoid cliche'.
As to "suddenly," it may seem like a strange rule. Isn't it important to know whether something happened suddenly, or whether it occurred over a period of time? Yes, but just as with adverbs and exclamation points, it should be clear from the context.
Consider The Goldfinch, by Donna Tartt, which won the Pulitzer Prize this year. I have it on my Kindle Paperwhite (a wonderful product, by the way), which gives me the ability to search it. I found sixty occurrences of the word "suddenly" in the 775 page book. But were they necessary? Here are two examples:
"Theo?" my mother said suddenly. "Did you hear me?"
. . . I was close to tears when suddenly I saw an inconspicuous door in the side of the gallery wall.
What if we take out "suddenly?"
"Theo?" my mother said. "Did you hear me?"
. . . I was close to tears when I saw an inconspicuous door in the side of the gallery wall.
Do you think it changes the meaning? Did the "suddenly" add anything? I don't think so.
In Doctor Sleep, Stephen King, who wrote a book called On Writing, uses the word twenty-five times in the context we're talking about, in a book that's a little less than 600 pages.
The hat woman disappeared and suddenly a crowd of concerned faces was gathered around him.
Do we need the "suddenly" in that sentence? What if we just took it out?
For whatever it's worth, Neil Gaiman used "suddenly" seven times in 246 pages.
The bottom line is that the word "suddenly" doesn't add anything, usually. Just say it happened.