You're probably correct that a significant raise in the minimum would make it more price competitive to further automate low skill jobs. But maybe the real issue is talking about why prices are so low, and not just wages. Prices for many goods are artificially low, and should be a lot higher. Look at the obesity problem here, and the pollution problem in China to get a handle on what low prices actually cost us. A great wage shock might be a bad thing in the short run, but I think it would be a good thing in the long run. It might help us to reevaluate what is important, what real prices are, and why we tolerate such social and environmental abuses all in the name of Black Friday sales.
I agree with a lot of what you're saying, but similar to my comment, both of what we think needs to be addressed will take a global conversation and cooperation at this point in our global economy.