Assuming I checked all the right majors at the Yale College site (I didn’t include CS except for EE & CS), it looks like in the Class of 2022, there was about a 62:24 ratio of employment (including researchers) to grad students (I am holding out all the small “other” categories). I have no idea how this compares to the “top” Engineering programs, but it confirms at least a good chunk of Yale Engineering grads are moving on to graduate programs.
Of the 62% employed, only 35% of them were employed in Engineering (not including research). I am going to guess that combination is low–that is only 22% going directly into Engineering jobs.
Research is another 15.4%, and there are some Data Science, Programming, Military, and Entrepreneur jobs that may be “engineering” jobs in the broader sense.
However, a whole bunch more were then in some sort of consulting/finance/business development/management job. Looks like at least 27% or so, more if you also toss in Sales or Advertising/PR. Again, I am going to guess that is relatively high.
In the end, I suspect Yale’s ambition is not necessarily to ever compete with, say, Stanford or Cornell in Engineering. But I do suspect they want to be good enough at Engineering that if highly-competitive applicants are at least thinking Engineering is a possibility, they won’t necessarily simply rule out Yale. And then what they do with that degree might be any number of things.