Cost disease isn't driven by a shared currency, but by a common labor market.

When hyper-productive sectors, say, tech in the Bay Area, start paying top dollar, everyone else in the same talent pool eventually needs to follow suit.

Even industries with stagnant labour productivity, like K-12 education, have to hike their wages to attract and retain staff. They can't offset these higher costs with efficiency gains, and that's where the "disease" kicks in.

If you think this is caused by a common currency, consider labour costs in developing countries which use the US dollar. Do those costs go up when labour productivity in the Bay Area goes up?