However I think this piece reflects a bit of ignorance with regards to the value one gains from a science degree versus a humanities degree. I'm speaking from the position of one who took a lot of English course work (particularly creative writing and critical theory) but dropped the second English major while keeping on with geology through a postdoc. I don't know how much this applies to an engineering degree as science shares more with the humanities than engineering does, and my experience with the engineering curriculum is limited to math/physics courses and having civil engineering students who took geology electives.
When learning a science, one generally learns about the history of the science and the process of societal knowledge-building through this lens. Though Douthat may decry a reduction of history to a 'litany of crimes and wrongthink', here we learn it as a kind of human Markov process with accumulating insight and wisdom, eureka moments and wrong turns, and how internal forces, hidden agendas and external shocks can promote and impede progress. The 'history and tradition' that Douthat feels are no longer valued in technocratic society is actually embodied in science's theory and practice--with the constraint that it is constantly tested, refined and improved (though not monotonically).
There is also a good amount of philosophy involved with working at the ragged edge of knowledge (though this may not really sink in until you get involved with research). It's tough to sift through and braid loose threads of truth, some of which may be based in logic and mathematics, observations, and insights from instrumentation and modeling that may be not yet be fully tested.
Additionally, there is a humility that accompanies the struggle to find knowledge and truth that may be unattainable, forever or at least in a lifetime. Anything that has happened on Earth over the past 4.6 billion years is within the purview of geology, but only events that have left a mark may be investigated. Given the finiteness of the Earth's surface and near surface, the vast majority of events have had all of their records erased and that bit of physical memory has been overwritten. Some questions are as unanswerable as the timeless questions of religion, though perhaps for different reasons. However it is probably less clear from the outset which scientific questions may be answered than which humanistic questions--as a practitioner you have to make the call whether to proceed and when to turn back (cue Kenny Rogers).
And furthermore, a lot of this occurs in an arena that has quite a bit less of the sort of moralistic/nationalistic/etc. status ranking that plagues the humanities currently. Jake Seliger is spot-on in his diagnosis of this in the humanities in the blog post he linked to in another thread. While there are certainly turf battles, issues with illogical attachments to discredited theories due to sunk costs and so forth, different theories of earthquake nucleation don't have the immediate implications for the status of different social groups (beyond researchers themselves) and it's not straightforward to moralize any of it. The different lenses that are applied to knowledge through different techniques (instrumentalists vs. theoreticians) are not so different than the different lenses of critical theory and modern identitarianism: What does this problem look like to a geophysicist who does seismic imaging, and what does it look like to a fault geologist, and what does it look like to a statistical seismologist? And while one group may have the upper hand in investigating a specific issue, almost everyone is working towards the same positive-sum goal (though the short-term scrabble for funding an influence is absolutely not positive-sum).
I think the society that Douthat fears is not 21st century science, but perhaps something more akin to early 20th century scientism--the technocratic philosophy that permeated Leninism, Modernist architecture and urban planning (Le Corbusier, etc.), Taylorism in management at all levels, and so forth. Inducting more college students into a discipline's quest for truth through experiment and falsification will not degrade our culture in the manner he supposes.
(And as a short personal anecdote: I decided to abandon the English major the day I went to Poetry at 10:30, in which we fruitlessly debated the word 'race' in a poem "literally" about a white girl seeing a black girl on the other side of some train tracks, after going to Petrology at 9:30 and working through the geochemical data from earth and lunar rocks that show when the moon was separated from the earth 4.5 billion years ago. Who exactly is pursuing truth and beauty?)