Having had to work with many people who either came from a school with very limited genEd requirements, or where some students found some loopholes to get out of them, etc., I can now appreciate those 'pain in the ass worthless' classes. I've strongly suggested to some of them that they go back just to take a few of those classes so that they (maybe) can see that it doesn't matter how fast their code runs if they can't work well and communicate with others (coders, engineers, HR, administration, customers, end users, etc) and technical writing actually has to be read and understood by those same others in many cases. But that's only one of many reasons that it makes sense to take them and actually expend effort on learning in those classes.
That said, I have to provide a couple of caveats. First, even taking those classes there are no guarantees that you will be a well rounded, socially apt individual capable of communicating with everyone with backgrounds from PHD's to GED's. Some will take the courses and either be incapable of assimilating the material or just refuse to. To some extent, that's where the socialization outside of class can help. In some cases, people are just narrow minded jerks and are basically content staying that way.
Second, we could have many pages of discussion on the general state of education in the US today and how many of those classes are in fact fairly worthless on many campuses. The bar has been lowered at the elementary school level which in turn forces the bar to be lowered in each tier up through high school, which in turn means that teachers of genEd classes at universities have to either lower the bar or fail massive numbers of students. At places where non-tenured teachers have their salary and/or jobs somewhat dependent on pass rates and student evaluations, the obvious pressure to drop the standards means that those students that are 'above average' will find the courses pretty lame.
My advice would be to take the genEd classes. Maybe reach out to some successful people in the industry and ask their opinion on which types might be most beneficial, ask recruiters or hiring managers what they look for as well. There are plenty of people in the various sectors of industry that would be happy to give their opinion.