There aren't many actual cordwainers around anymore. Most of them are just shoe repair places that are rarely called upon to do anything demanding. They can put on a topy, stretch a shoe, replace a toplift or even a stacked heel, but actually re-stitching a sole is beyond most of them.Many cordwainers in Melbourne Australia don't want to machine stitch shoes anymore because they don't think it has much benefit over glued soles.
I had a pair of Loake plaintoe bluchers - thankfully, bought on deep discount from Herring Shoes - that needed a resole. I took them to my local shoecare place in the city and asked them if they could resole a Goodyear-welted shoe and they said they could. When I got them back, they'd stitched on a new sole by putting big stitches all the way through the shoe, from the inner through to a channel they'd cut in the bottom of the new sole. I was quite literally speechless when I picked them up.
I don't put a Topy sole on all of my shoes, but in Australia I really think that it is a good idea to do so. Otherwise, when soles wear out, it is almost impossible to get the shoes properly resoled here and the only option is to send them overseas, which is prohibitively expensive.