Much of the other stuff can easily be self-taught given a strong/exceptional foundation in critical thinking ability, and it can be used to great advantage in differentiating yourself from your peers.
Right, because they certainly don't teach that in engineering school.
Personally, I think everyone should learn at least the basics of modern Algebra (not high school stuff, but: groups, semigroups etc.), Topology etc. (Note that I did not get an education in either Physics or Math, but am jealous of those who did)
"Critical Thinking" (and its development) is perhaps more nebulous, but I imagine that it comes with extensive work on proofs and problem-solving in more abstract situations.
* Mathematics is entirely about proving arguments and solving problems within logical systems. * The 'hard sciences' (esp. physics) are about working within a theoretical (often mathematical) framework and testing it with experimentation.
Contrast this to engineering disciplines, or even medicine, where the focus is on gaining knowledge which you can use to solve problems. It's problem-solving, but doesn't have much of the scientific method about it.
Not to say that engineers are necessarily inferior - there is a foundation that I'd say most don't have though in comparison.
Further, the entry level physics & math classes at my school were the exact same classes that physic & math majors took. This clearly isn't universal, but you can't make a generalized statement that entry level physics & math classes are harder/better than they are for engineers. Physics 1,2,3 is Physics 1,2,3 (101,102,103 in uni numbers)
I could insert some snark comment about if they were truly better at critical thinking, they would have pursued a degree that was more easily marketable, but that's besides the point.
Engineers have skillsets that are in high demand, and that's why they're valuable degrees.
Is critical thinking a part of that, probably. Is it as valuable from a Math/Physics major? We'll just let the market decide.
Companies that hire pure talent often have went after top math & physics types, especially Wall Street - that's no secret, and this has been true for decades. They are extremely marketable degrees, and attractive to any company when combined with domain knowledge in other fields - to give some examples of some of the things that some of my peers are doing who possess those degrees, they include public policy, programming, data science, statistics, academia, teaching, economics, patent law, and finance. The versatility is what is valuable, not necessarily the domain knowledge of math or physics itself, although that could be helpful too (i.e. the NSA, the largest employer of mathematicians, who often train them as programmers afterwards).
It doesn't hurt that they are usually amongst the top degrees to have in various charts, and related careers to those skills are similarly rated very high (e.g. statistician being #2). Engineering (most notably computer science) has had a surge as of the past decade due to the talent crunch and surge in innovation in software, but at the top, many companies still are very interested in more traditional candidates who show initiative since you can teach someone many things if the person is well grounded in fundamentals, but you cannot necessarily do the reverse as easily.
It does take some self-investment, but you have a flexibility not afforded by most disciplines - math & physics best prepares you more generally if you apply the lessons. I feel confident innovating/performing in many other aspects as well, but I chose software engineering & the developer crunch chose me.