One thing that always seems to be at a disconnect between the economic literature and policy makers is the economic context of the raise in wages. Even those economists that have bought in fully that minimum wage increases don't typically decrease employment will have several caveats to that statement, usually worded in the form of "small increases in the minimum wage". That is to say that there are often small inefficiencies in our current markets which allow employers to reduce wages in cartel-like fashion, and small increases in the minimum wage can claw some of that back in favor of the employees at the expense of employers' economic rents, but not at the expense of economic output. But large increases in the minimum wage absolutely can jump the shark, decreasing economic output by effectively making low margin sectors untenable entirely. If that weren't the case, we would be able to raise it infinitely without any negative effects, which is absolutely absurd (and unfortunately that is the takeaway that ideologues often get from reading abstracts).
A more useful economic model would go a step further than just saying "you can raise the minimum wage without harm to the economy", by incorporating econometric analysis which can accurately predict when and how much you can raise it without incurring economic harm.