I heard you out. However, most of your arguments make no sense. Allow me to explain.

One of the first things you mention is to take Yale's name out of the question. While prestige does matter in certain fields, I generally agree with this completely. Let's keep this in mind as we move on.

Next, you acknowledge that Yale has an excellent undergraduate experience, but claim that it is not relevant in making it a "top school". Why is this? Do you believe that college is purely academic? When choosing a college, do you not care about the undergraduate experience? If so, then I understand why you think this way. Perhaps, then, in your evaluation of colleges, you only consider academics, in the context of which the rest of your post follows. However, I can tell you that most people do not think this way. Almost all students desire a great undergraduate experience, and so here the title of your post, that Yale is objectively among the worst Ivy League schools, is already invalidated. However, it still remains a possibility that you have concluded that Yale is among the worst Ivy League schools for you. So let us continue to see if your analysis makes sense.

You continue by claiming that every top school has a specialty. While I do not agree that such a feature is necessary for a so-called "top school," let us entertain ourselves with this idea.

The first school on your list is Harvard. The first thing you note about Harvard is that "it's Harvard." I would like to remind you that we are taking the name of a school out of the question. Next, you note the strength of Harvard's graduate programs. This is true. However, you state that Harvard has the best medical school, and "arguably the best law school." I will argue that Harvard also has "arguably the best medical school." You cannot say that Harvard definitely has the best medical school without saying that Yale definitely has the best law school. Both of these programs are considered to be the best in their respective areas. You continue by noting that Harvard's graduate strength trickles down to its undergraduates. This is difficult to measure, and is certainly not a major factor in an undergraduate education. Finally, you note once again that Harvard has the biggest name. While this is true, please remember that we are not taking a school's name into account. However, if we are to do so, Yale's name is not very far from Harvard's, and arguably bigger than all the remaining schools on your list.

Let's continue to Princeton. You note that Princeton and Cornell have the strongest STEM programs in the Ivy League. While both of these schools are noted for their STEM focus, it is difficult to understand how you reached the conclusion that they have the strongest STEM programs in an absolute comparison with other Ivy League schools. The quality of the undergraduate STEM programs, overall, is fairly close among the Ivy League schools. It would be ridiculous to assert that there are major educational differences, simply due to some rankings and general perception. Next, you state that Princeton carries more academic prestige than Yale. This is wrong. I would also like to remind you again that we are not considering name in the first place. Lastly, you note the uniqueness of Princeton's undergraduate focus, specifically in the fact that they lack many graduate schools. This is true, and is certainly a distinguishing feature of Princeton. However, Yale is perhaps the second-most undergraduate focused of all the schools on your list. For example, all professors are Yale are required to work with undergraduates.

Your analysis of Columbia is fair and accurate. I do want to point out that Yale has easy access to New York City, as well as Boston.

Your description of Penn is accurate as well. The Wharton School is probably the best example of your so-called "niches." However, I do want to mention that you note that Penn draws students away from "HYP." Note that you yourself included Yale in this list of supposed "top schools."

You continue to claim that Stanford is arguably the "best all around school." Please note that you were originally discussing school specialties, not their well-roundedness. The rest of your analysis is reasonable, although I would like to point out once again that the STEM programs at all of the schools on your list, overall, are fairly close.

The same note applies to MIT. It is a fair argument that MIT is clearly above the other schools on your list for computer science and engineering; however, this is not true for STEM in general.

Your UChicago analysis is excellent.

Your notes on Northwestern are fair as well, although I do not see the "niche." I would also like to point out that you used the acronym "HYP" once again.