Pretty much ANY goat (or cow) *can* be used for milking. But the tiny little pygmy goats, and the smallest Dexter cows are such a PITA to milk, most people don't bother.

There is a reason the various breeds were developed. And you can't discount the literal centuries of selective breeding behind the dairy breeds of both species, in terms of everything from production, ease of milking to disposition.

When our Dexter/Jersey heifer calved, she stood well for milking (by hand and then machine) from the first day. She kicked a couple of times in the second week, when her teats were getting a little chapped and sore, but she was extremely easy to train to milk. The Dexter cow who had Miracle, OTOH, would stand to be milked for a couple days, and then one milking would suddenly throw a fit and kick the heck out of whoever was milking.

In the breeds which have been used for dairying extensively, the animals and lines which aren't cooperative have generally been culled out. These animals have also been bred for extended lactations (still producing lots of milk through 8 months or longer, if necessary) where most meat breeds produce enough for their offspring and then quit.

But essentially, you can milk or eat any breed of cow or goat.

Summerthyme