I know that in economics it is difficult to do proper studies hence the "dismal science", but my understanding is that most economists agree that minimum wages don't work right? So why is it still pushed? Shouldn't we "listen to the experts"? Besides there are other tools like the EITC.
There's "economics" and then there's real world effects. Take some time to study what actually happens in countries with a living wage.
In Denmark there’s no minimum wage, yet people are paid well. The wages are agreed upon by the employeers organisations and the unions. It does set a minimum wage per industry, but the important part is that it’s not set by politicians who have no idea what the real world looks like in each industry.
A universal minimum wage risks being to low for one industry, while being to high for another. It makes more sense to do collective agreements per industry, and by having the unions act on behalf of the employees you ensure sufficielt leverage against the employers.