Are there skilled professionals who will supervise unskilled DIY labor?
DIY projects, probably not. The price would negate any financial benefit of doing it yourself in many cases. That said, I've resorted to the beer-for-services approach many times for electrical and plumbing consulting visits from friends and relatives, which is usually win-win.

Major remodels and builds, yes. In fact, my family's company offered such a service at one time. We'd make regular trips to your jobsite and create reports of progress and areas of concern. You'd be the general contractor of record. It was a way to save tens of thousands of dollars on a project, yet still have peace of mind that it was done well, and it helped grease the wheels with inspectors and sub-contractors. The service probably falls under the umbrella term "building consultant", but there may be others.