Learn English – Is “burst oneself laughing” a valid expression

Yes, as in "a robber would rid you of your money."

This is, as you noted, a very American idiomatic phrase which apparently dates from the 1970s. One dictionary includes the phrase in its definition of good, but notes it is American English. An idiom dictionary further refers to the phrase as a cliche. Interestingly, the only idiomatic definition they give is from the McGraw-Hill Dictionary of American Idioms and Phrasal Verbs.

One should be cautious when using this phrase, however. A blog found that the British explanation of the origins of the phrase were:

Have a nice day

Meaning: A salutation, ostensibly to offer good wishes. In fact a banal and insincere form of words given to anyone and everyone. Evidence of the meaninglessness of the sentiment is the fact that it is even used last thing at night when the opportunity to have a nice day has all but disappeared.

Origin: US origin - around 1970s.

The blogger notes that British people may construe this parting phrase as highly sarcastic, so it may be best to keep its use to the American English arena.