That attribution to Twain is bogus. I believe it started as a letter to the editor in some mid-20th century magazine. Let me see if I can dig up the citation.

(Edit 2: the Economist came later! see downthread)

Edit: the joke originated as a letter to the Economist in 1971: https://web.archive.org/web/20200807181810/https://lettersof.... The classic internet version (referencing the European Commission) was a later rewrite—no idea by whom. It's interesting that the original was a UK in-joke ("Haweve, sins xe Wely, xe Airiy, and xe Skots du not spik Ingliy") but the rewrite became more outward-facing, a sort of Euroskeptic joke when light humor about that was still possible (I got it in an email in the 90s), as well as quite a bit funnier.

Misassigning it to Mark Twain is not surprising, because all great quotes by obscure people get reattributed to famous writers over time. Also, Twain wrote a famous and funny essay complaining about German (https://faculty.georgetown.edu/jod/texts/twain.german.html), and he was interested in alphabet reform too (http://www.online-literature.com/twain/1322/).