When you are optimizing for employment ratio. Zero minimum wage gives 0% unemployment and creates millions of jobs. Those are some great achievements to have if you're running for reelection.
There is no reason to support a minimum wage if you don't care about quality of life.
Technically true, but the combination of a generous welfare system and powerful unions means that there is a de facto minimum wage.
No one is going to work for much less than they'll get from unemployment, and just try starting a company paying less than the union collective bargaining rates and see how long it takes before a bunch of thugs harass you out of business.
The unemployment rate is a lot higher amongst MENA immigrants and their children than amongst the natives. This is a general finding and not in any way unique to Sweden. What is close to unique is the sheer number of low-skilled immigrants relative to the native population.
An official minimum wage is not the only way to create a de facto minimum wage. Welfare subsidies is another. Strong unions is yet another. High contributions to medical insurance and pensions paid by the employer is yet yet another.
There are also others way to create high unemployment: making it very risky and expensive to get rid of mishires or to reduce headcount if the company isn't going so well. Making management more difficult once the headcount reaches a certain level (because of unions or the creation of employee boards mandated by law) -- that leads to companies trying to stay below such ceilings. Others would be salaries/pensions/benefits tied to how long one has worked for the same company -- which discourages moves to other companies (that might fit ones personality or talents better -- or that has better management). The housing market also has an influence: there might be opportunities in a different city but how easy is it to move? It is relatively easy if you rent your house or appartment. Not so easy if you own it, especially if selling it means you realize a loss. Lots of laws and regulations in a country influence the structure of the housing market (how liquid it is, what loan types are available, how many people rent instead of owning, etc.).
There is no reason to support a minimum wage if you don't care about quality of life.