Au contraire! There are lots of Cotswold sides who use English concertinas alongside melodeons - I agree the Anglo (being very similar to the melodeon) is favoured as a solo instrument for Morris.The side I play for (Earl of Stamford) usually has Alan on Melodeon, John on English, and me with the accordion.
John has large wrist straps to facilitate playing his English (a Wheatstone) standing - I've never found it to be a problem myself.
That way we are able to vary the sound, and it allows a musician to dance if he chooses.
As to the chemischnitzelwotsit - it's a new one on me! It sounds more like a Japanese suicide pilot!! Are there any over here in England? Bandoneons I know - a sort of cross between a melodeon and an accordion...
Anyone got pictures?