In my experience, there's no such thing as unskilled labor, only labor in which the skillset is unappreciated. Just because a job may require little to no mental presence, for instance, doesn't mean it isn't physically demanding, and likewise in converse. I'd like to see your ditch digger try to code a website while your software engineer takes a stab at digging ditches at the same rate as they did, for example. Both will probably suck at it. (Plus, in what reality is a software engineer making only slightly more than $15/hr? If that's you, you need to demand a raise because your time is being undervalued)
Plus, I'm a bit peeved that you're tossing in the whole "if we pay the lowest wage-earners more, then they'll be making just as much as people with slightly higher wages, and that's unacceptable!" mantra, because that is EXACTLY what people with power always say to make sure that no one ever is payed more for their time, and you're just another person who's swallowed that line and is feeding it back out. You act as though placing more value on one person's job somehow takes value away from someone else's, as though value is a scarecly limited resource, but it's not; if the lowest earners are paid enough to actually feed themselves while paying rent, a few things will happen: jobs will open up, allowing for more people to enter the workforce (there are a LOT of people working two and three jobs just to get by, in my eyes that's unacceptable), wages will go up incrementally all the way up as laborers in higher positions demand wage increases and finally get that bargaining leverage, and the local economy will improve as more of the people who were just barely getting by in the lower-middle class can finally afford some non-essential niceties.