Yes John, you are right there.
As for playwrights, since Shakespeare was English and has had such influence on the language, I was wondering if lines from Macbeth may have introduced the idea of ‘scotched’ and his rather comical portrayal of the Welsh language led to that entering the ‘collective consciousness’.
English also has a range of derogatory terms about the Dutch, although I am not aware of anyone in the Netherlands taking offence. dutch courage, dutch oven, double dutch, dutch uncle, going dutch…
Many of those, I think, are corrupted from Deutsch.
Quite possibly, those of American origin, cf. Pennsylvania Dutch, and some date back to English - Dutch military conflicts in the 17th/18th centuries I believe
My husband, Mr Welch, is certainly aware of the roots of the phrase!
I wonder how many people ever think about it, though, even if they use it (do younger people?) A bit like “foot of the hill” where the metaphor has sort of become plain speech, maybe. I think people would be interested to learn about the assumptions in its origins.
I doubt if youngsters would use “welch”.
Now I’m frightened to ask about foot of a hill, but bank foot (and dan y banc) are well established historical names as far as I know. Also bar or barr in both languages (but of Welsh/Brithonic origin) for the summit.
Also in civil engineering there is the heel and toe of a batter (bottom and top of a man-made slope) 
A coworker (in America) innocently used this phrase in a presentation a month or two back – and another coworker was so bothered by whether it’s an ethnic slur that he mentioned it gently to her. She was horrified, and came to apologize to me.
This led all three of us, then, to research the origins of “welching / welshing on a deal” . . . and according to a leading theory, it originates from dishonest English bookmakers fleeing across the border from England into Wales in order to avoid paying out winning bets. Fascinating…
https://www.phrases.org.uk/bulletin_board/1/messages/2119.html
So it’s still an ethnic slur, then…?
Facetious answer: Yes, just as “knocked for six” is an ethnic slur against cricket balls.
Genuine answer: Interesting. You could say that it’s a slur against the English, although the alleged origin seems less about ethnicity than about England being the only country with a convenient land border with Wales. Or, more realistically, that it is a bit of a slur against Wales for being a backwater / mountain fastness into which people can safely disappear.
Then again, that last is something of which Welsh people are justly proud. Anybody seen Owain Glyndwr lately? 
Still, a phrase that I think is better avoided than used.
In the United States, Americans of Welsh ancestry view it far more seriously then we home-grown Welsh perhaps do, Baruch. In fact, a few years ago they launched a public campaign to have it consigned to the language-dustbin.
But America uses, or used, it more than English people do, so I don’t let it bother me overmuch because I don’t think people from over the dyke are being consciously offensive about Welsh people when they use the expression.
I’ve lived in Eastern England since 1948 and I couldn’t begin to count the number of anti-Welsh comments I’ve heard - and not just in the rugby season, although it’s worse then. As far as I’m concerned it’s like water off a duck’s back.
There was a brief ad campaign by Carlsberg about 25 yrs ago that I remember seeing on buses, where instead of their usual slogan ‘probably the best lager in the world’ they went with ‘definitely the best lager in the world’, but subverted it visually in some way. One was printed along the mid-line of a couple of red fish – presumably herrings. The other was a couple of Edam cheeses with something like “Carlsberg: gewis het beste laager ter wereld!” (I’ve probably misremembered it) on the rind. No English: just brand recognition; and almost the only adverts ever to stick in my mind so long.