Remember that in earlier times 'welsh' had a much broader meaning than just 'them from over Offa's Dyke'. It basically meant foreign; and, at least until recently, and outside of big towns, 'foreign parts' meant anywhere past the next village up the road.
I agree regarding the percieved difference between 'welsh' and 'welch' but I would suspect this is victorian pedantry. Using spelling to derive the etymology of words that were in use in days when most people couldn't write, and if they could, had no concept of conventional spelling (those in their 40s and 50s now, taught ITA (a phonetic alphabet), where the sounds available had no relation to spoken english, may have felt themselves in a similar situation), seems a pointless exercise.