If one looks at past history, it could be argued that Yale is one of the least robust engineering programs in the country.
It started out with what has come to be called “The Yale Report of 1828”. Four years after the founding of RPI, at a time when the country was trying to gear up for the industrial revolution, Yale declared that educating their clientele (the leisure class) should have nothing to do with anything that required the use of the hands (other than croquet). They argued that studying dead languages was a better way to prepare for the future than studying technology.
In the report, Yale (which was clearly behind the times in science) talked about the “furniture of the mind” and presumably was concerned that decorating the mind with modern furniture would be in poor taste given the faux Gothic architecture of the campus. 
Ironically, in 1863, Yale was the first college to take funding and operate under the terms of the Morrill (land grant) Act, which was intended to fund the creation of agriculture and mechanic arts (engineering) programs. After years of complaints around performance, in 1893 Yale’s land grant status was revoked, making it one of three schools in the Northeast (all members of the Ivy League) with this distinction.
https://today.uconn.edu/2012/09/land-grant-status-acquired-after-yale-storrs-controversy/
Cornell (which was founded in 1865 as a land grant college) was able to maintain that status.
Throughout the the 20th century, Yale’s administration struggled with the concept of engineering doing away with the Sheffield School in 1919, then re-establishing a school of engineering in 1932 only to totally neglect their undergraduate programs resulting in a loss of their engineering accreditation. in 1966. After nearly two decades of rebuilding, they were able to regain accreditation in 1984 only to have the provost propose that engineering be eliminated in 1992 to save money (presumably to fund dead languages in order to better prepare their students for the 21st century innovation economy).
Yale did not approve the proposal (so they still have some engineering. More recently they have managed to increase funding, but who knows what the future will bring.
https://seas.yale.edu/i-am/alumnus/yale-history-blog/post-world-war-ii-era