What is the experiment you're proposing? I didn't follow.
What about just measuring the ROI of the degree?
https://www.nytimes.com/2021/08/13/your-money/college-degree...
"All of the largest programs in electrical and communications engineering, for instance, allowed most of their graduates to recoup their educational investment in five years or less. But many programs in some fields, like drama and dance, show no return on investment, the report found, meaning most of their graduates are earning less than a typical high school graduate."
So this study more or less backs claim that some degrees offer a positive ROI while others do not. As to whether or not a given degree is "worthwhile," I'd leave that as an exercise for the reader. :)