Given that, I can't help but think there's something wrong with the analysis. I have no domain expertise to tell what it might be.
But in this case, the author is complaining about the tax law associated with tipping and not with the minimum wage hike in itself. Doing away with tipping will be great on a societal level but reforming the tax law will do a lot to keep restaurants from shutting down in the short term.
Like, if everyone knows that the wait staff gets paid $15/hour then wouldn't there be less pressure to tip, say, 20% on meals? If all wait staff received at least $40/hour then I'm sure that most people simply wouldn't tip.
And how would this change, to include tips as part of wages, help the "near-poverty cooks and dishwashers"? Are the businesses on the knife-edge of solvency that they simply can't afford to pay the back-end staff more? It seems more likely that the savings will go to the restaurant owners?
You mentioned socialized health care. Doesn't that also affect the labor costs? That is, the US government already pays more per capital on health care than just about every other country - then there are private health care plans on top of that blowing the costs sky-high. By switching to socialized health care, it should lower the overall healthcare costs, so make it cheaper to employ people ... unless of course the restaurants currently don't provide reasonable healthcare coverage to their employees.
If you look at number of McD's by country, Denmark has 1 location per 64k people while US has 1 per 23k [0]. Also some of that is preference.
I'm not also not sure where you got the $20/hour wage for Denmark:
Denmark Minimum Wage: None; instead, negotiated between unions and employer associations; the average minimum wage for all private and public sector collective bargaining agreements was approximately DKK 110 (nominally $16) per hour, exclusive of pension benefits [1]
[0] https://en.wikipedia.org/wiki/List_of_countries_with_McDonal...
[1] https://en.wikipedia.org/wiki/List_of_minimum_wages_by_count...
> Statistics Denmark is the government agency that tracks labor information. For the category of food service counter attendants, the annual pay in 2012 was over $41,000. That is for all companies, not just McDonald’s. On an hourly basis, that translates to about $20 an hour.
This compares not 'gross pay' but 'gross pay plus tips'. Of course a more complete analysis would also include benefits and payroll taxes.
Note however that my question does not depend the raw numbers. It holds even with a "less severe" difference.
It would only be a problem if the tax level in Denmark was high enough that the difference is inverted, which I do not believe to be the case.