The MIT paper pegs broadband at $60/mo which translates to about $0.35/hr in the living wage. MIT also includes a smartphone prorated over three years with unlimited talk and text and between 10-15 GB of data, I think it comes out to about $48/mo for a cell phone (+$0.27/hr in the living wage). I wouldn’t include broadband or cellular data plans because I think these are not essential (unlike a prepaid voice/SMS plan). We can start a different topic if you want to debate that point. Assuming I can shave eight or nine dollars off the monthly phone bill, drop the broadband, there’s about $0.40 of the difference.
MIT’s living wage health insurance component (based on employee contributions to employer-sponsored plans, from this table) comes out to $128.58/mo in my region (+$0.75/hr in living wage). I had used $10/mo ($0.06/hr) based on individual coverage in the marketplace, as advertised in recent healthcare.gov commercials. So there is another $0.50 difference.
They also include about $426/mo in transportation costs for my region (+$2.45/hr in living wage). That is also based on BLS Consumer Expenditure reports of transportation costs by household size, adjusted for regional variances. I don’t think this is necessary. Owning a car may be necessary in many places or for various jobs but it isn’t necessary here for most minimum wage jobs I can think of. People making minimum wage can (and around here often do) use either public transportation, or a bike, or walk, or some combination. A bike can easily be prorated to under $0.20/mo, and here unlimited bus fare comes at $30/mo. So in transportation I find a difference of about $2.27/hr.
$2.27+$0.5+$0.4=$3.17, which is more than the $3 difference between $13 and $10.
The goal is not simplification. It would be immensly more simple to have a single national minimum wage at $13.10 or $15. As stated in the OP, the benefit of local minimum wage ordinances is that it would be easier to pass local ordinances than national legislation.
~Max