The minimum wage has jumped up several times in the past due to government updates, and it has gradually shrunk over time due to inflation, and neither of those things has been particularly correlated with employment rates
There are better policies to protect poor workers, like reducing taxes on the poor or allowing government welfare for those with jobs. These help workers without distorting markets and hurting workers. The only case minimum wages are useful is if all the alternatives are impossible.
I don’t understand the link to medical insurance. In my country poor people get free healthcare. Low wage earners still get taxed, which I think is immoral and is exactly the kind of policy discussion that minimum wage proponents smother.