Why do we say "Good riddance to bad rubbish"?

Meaning:

An expression meaning to be glad to be rid of someone.

Background:

According to The Random House Dictionary of America's Popular Proverbs and Sayings, the earliest known usage of this expression in the USA is in the Assex Gazette in 1771. Finding no record for the Assex Gazette, we wonder whether this is a misspelling and should read Essex Gazette (a paper of this name was in print at that time in Salem, Massachusetts).

Perhaps the more interesting topic is the use of riddance. It's a word that has fallen out of use these days pretty much across the board except in this expression. But, according to phrases.org.uk, it used to be a general-purpose noun meaning "deliverance from" or "getting rid of" that was in use from at least the early 16th century, as seen by John Rastell's poem, Away Mourning:

I haue her lost,
For all my cost,
Yet for all that I trowe
I haue perchaunce,
A fayre ryddaunce,
And am quyt of a shrew.

Shakespeare seems to have been the first to combine "good" with "riddance" in his 1606 play Troilus and Cressida in which Patroclus responds to some verbal abuse from Thersites with a pithy, "A good riddance."

"Bad rubbish" appears to have been added around the late 18th century, as previously noted, and definitely by 1805 when it was used by Tobias Smollett in a blistering critique published in The Critical Review:

But we are sorry ... to consider Mr. Pratt's writings as 'purely evil' ... we should really look upon this author's departure from the world of literature as a good riddance of bad rubbish.

The Mr Pratt in question appears to be Samuel Jackson Pratt (1749-1814), a prolific English poet, playwright and novelist whose life was tainted by scandal (living with an unmarried woman) and is remembered as the first English writer to treat the American Revolution as a legitimate topic for literature, and as an early campaigner for animal rights. What he had done or written at that particular time to be on the receiving end of such vitriol from Smollett is unclear.

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