One labor market indicator that is strongly correlated with upward mobility is the teenage labor force participation rate. …This could be because formal jobs help disadvantaged teenagers directly or because areas with good schools and other characteristics tend to have more teenagers who work. In either case, this finding mirrors the general pattern documented above: the strongest predictors of upward mobility are factors that affect children before they enter the labor force as adults. 

- Chetty et al (2014)

Targeted tax credits do a better job of reaching the poor than minimum wages do. … Low-paying jobs requiring low skills are the jobs most likely to decline with increased minimum wages.

- Neumark (2014)

Employers are more willing to give someone a chance - that is, hire them - when the cost of failure is manageable. Failure in this context means a less than optimal employee who quits or is fired. The cost of failure is how much that employee has been paid. Raise the cost of failure and employers are less willing to take risks on job applicants who have a bunch of minuses: youth, lack of experience, poor English, low education level, erratic work history, etc. That's why a mandatory high minimum wage can hurt the most vulnerable workers.

Getting, keeping, and mastering a job is a huge confidence-building experience. Hope falters without confidence. Effort falters without hope: if nothing will come of my effort, why try?  Chronic unemployment zaps the will and can lead to a downward spiral. That’s why it's so important for employers to be willing to take risks on 'non-optimal' job applicants. Minimizing the cost of failure - an employee not working out - incentivizes employers to take such risks.

Shitty fast-food and retail jobs are dead-ends for some; for others, they're a start: the first step to a middle-class future (at the very least). If you require all jobs to pay a "living wage", then you may be closing doors to those that need the most help: the young, the low-skilled, and those who have stumbled but keep trying. 

References:

Chetty, R., Hendren, N., Kline, P., and Saez, E. 2014b. Where is the land of opportunity? the geography of intergenerational mobility in the united states. The Quarterly Journal of Economics (2014) 129 (4): 1553-1623.

Neumark, D. Employment effects of minimum wages. IZA World of Labor 2014: 6 doi: 10.15185/izawol.6 https://wol.iza.org/articles/employment-effects-of-minimum-wages