The story
In 1819, Charles Lamb wrote in a letter to Wordsworth: “I will never write another letter with alternate inks. You cannot imagine how it cramps the flow of the style.” Lamb’s letters were published in book form in 1837 and saw several editions and reprints. The letter was also included in volume 7 of the 12-volume book The Life and Works of Charles Lamb, thus appearing again in print at the beginning of the 20th century. It was again included in volume 6 of The Works of Charles and Mary Lamb, which was first published in 1905. It is possible that the idiomatic use, which dates from the early 1900s, originated with this passage by Lamb.
Etymology from Wiktionary, CC BY-SA 4.0.