Early on, there were some valid reasons for it...
Local Franchisees often produce better results and are more "in-tune" the the local market they're catering to than a corporate HQ employee 600 miles away who has no familiarity with the town. (although, the modern age has probably changed that dynamic just a bit)
What makes that model tricky for things like these min wage mandates is that people who aren't familiar with that model just assume "Oh, McDonald's, that's a mega corp, they can afford it, this is a great idea", when in reality, the person who actually owns their local McDonald's location is a person who's 200k in debt and only netting about 90-120k year for their first 5 years.
Fun story: Two of my buddies from college went in on a DQ franchise together some time ago (DQ is actually owned by Warren Buffet's company -- factoid), however, Berkshire Hathaway aren't the ones covering the costs of day to day operations. It was a lot of work and hassle (as one would expect when 75% of ones employees are high school kids), and when they finally got tired of it and sold it, all said and done after paying back the loans, I think they maybe did a tad better than breaking even on it? -- but it was by no means the "cash cow" they assumed it would be. They certainly weren't living high on the hog.