What kinds of consumer goods? When I lived there, it seemed reasonably cheap to me. Groceries were about normal from a US perspective, and rent in Copenhagen was quite low for a major city (~$1250/mo for a nice 2bd in a central part of the city). Some things varied, e.g. pork was very cheap, while fresh fruits were often expensive, but that's more a question of geography than anything else. Beer was exceptionally cheap, like $4/sixpack type prices. Fast food was on the expensive side, and labor costs are probably a part of that. Nicer restaurants were normal by American standards (expensive compared to Texas, cheap compared to SF or NYC). Overall I think my cost of living was lower than when I lived in the SF Bay Area, by a not-trivial margin.

And yet Danes can somehow still afford them.

I live in Norway where many of the same conditions pertain. I suspect that one reason for there not being a minimum wage here is that unemployment is low, which means that you have to pay a reasonable amount in order to get someone to work for you.