I think there are reasons to have a very STEM focused education, and equally good reasons to have a more rounded education. Every subject that is taught is important, because if it wasn’t, it wouldn’t be taught. Of course, that doesn’t mean that every subject is equally important for every person, but in general, having a strong foundation in many areas will be useful.
In some ways, it’s similar to what we try to do on our team (or at least what I think we should try to do). The year that I joined, many rookies had the tendency to focus on one area very early on, which is what I did with CAD. It was a great experience, and I definitely don’t regret choosing it, but I do regret that I didn’t get to work more in other areas. For example, although I have a general idea of how the electrical system on our robot works, I have no way of knowing if the way we designed it is best or how certain decisions I made about our baseplate it affects it. 
That said, there are many reasons that going in depth into areas can be very nice. My parents based my curriculum very heavily on what they knew from Singapore (I’ll explain a bit more later), which not surprisingly had a very strong STEM focus. Math would be be probably the only subject my mom never let me decide when/how much I wanted to do, although I did indirectly decide the pace I would learn it at. For several years, I focused only on subjects that we had workbooks from Singapore in: math, science, English  , and Chinese  with a stronger focus on the first two. The one main exception to this was reading. Until high school, I read a few hundred books a year (once I counted, and it was ~5bks / wk or ~260 bks / yr), mostly fiction but in almost any genre. 
I don’t feel like that focus on math/science has hurt me with humanities subjects, or at least not to a degree that I’ve noticed. But I also don’t see the same lines dividing them that some people–like my parents–draw between them. I’ve always used the same ways of thinking and reasoning in all subjects. I approach English essays very similarly to my math homework, and I haven’t heard complains from teachers in either subjects. However, I personally believe it’s far easier to apply a given skill from STEM into humanities than vice versa, the one main exception being communication (which is more a soft skill than something studied in school anyway, in my opinion). Therefore, although I think a well-rounded education is useful, I believe it can also be easily achieved after a focus with STEM. If I had to point out the one thing that has helped me in all subjects, it would be my mom’s unrelenting push for me to do well in math followed very closely by all the books I read.  Math taught me how to think logically, and reading taught me to see other viewpoints, and both have been extremely valuable skills.
I personally think the largest issue with education in many countries, but US in particular, is they’re not teaching students to think. The skills necessary to do well on the math section of the STAR test could be easily replaced with memorization. There were no word problems to decode, no multi-step questions to work through, and no combining of skills necessary to see how different theorems/rules work together. (Yes, I know that’s what Common Core is supposed to fix. But honestly, asking people to “explain” what they do isn’t any better and I don’t see it as much of an improvement). Math can require critical thinking skills, but not if it continues to be taught how it is now. The English, science, and history sections, from what I remember from 8th grade STAR testing, weren’t much better. All could be done with pure memorization and no actual understanding/analysis was necessary. Whether US decided to become more focused (e.g. STEM), stay rounded, or even scrap subjects for general concepts (like Finland), the issues with education will continue until they teach thinking, not memorization. (and until the culture here changes to put education as a priority)
Note: I’m basing a lot of what I’ve written below on my own education, which I should probably explain a bit. I’ve been homeschooled since 2nd grade, when my parents combined other activities with workbooks from Singapore, where they both grew up. For later elementary school and part of middle school, I roughly followed the Singapore curriculum in math, science, and English (and to some extent, Chinese). Just to note, though, while my parents emphasized the material, they didn’t focus on testing to the same extent (e.g. I did some practice PSLE / O-level tests in some subjects, but my actual score wasn’t that important to them). In later middle school, we started turning towards the US system, and for the first time since 1st grade I got to deal with it.
 Design is probably the area in mechanical (at least on my team) that has the most overlap with other areas. For example, I’ve heard girls in fabrication comment that they understand even less about areas that don’t directly affect them.
 Strangely, I’ve found the workbooks I did in Singapore for secondary 1 or 2 to be harder than any English test I’ve done in the US, including AP English Language, so I’d argue US isn’t that well rounded at least in that aspect. Also, it’s probably worth noting that since Singapore uses the British system of spelling/grammar, it is very confusing to have to switch between them and I therefore wouldn’t recommend it.
 Chinese was probably the only subject I never stayed near my grade level equivalent in Singapore with, and I am nowhere near their standards on it.
 I read mostly historical fiction until 6th grade, fantasy in 7th and 8th, and science fiction / classic dystopian novels after that. Despite what my mom says, I still believe there is a lot to be learned in every genre including fantasy. Fantasy was when I started exploring what in life really mattered, what would last, and why certain ways of thinking didn’t work. Exploring political systems between different novels led me to dystopian classics (1984, Brave New World, Fahrenheit 451, etc. (note not Hunger Games)) and a long obsession with comparing them to various civilizations.
 I’m probably understating the value of reading since it’s less measurable. However I still believe that math and reading gave me a stronger foundation than if I had followed a split-subject path. I’d argue that the ability to see other viewpoints is something that only parents can really influence, though, and critical thinking is the one that needs to be taught.
Summary (and to answer the original question): like anything else, a purely STEM education is not bad, but it needs to be done well, and it’s not the only way.