Health-
Sorry, but I think you have misinterpreted YU.
1) As another poster mentioned above, other than the slogan “Torah Umadda” nothing unifies YU. If you ask each of the Roshei Yeshiva what that slogan means, you will get a different answer from each one of them. Therefore, it is inaccurate to say “YU has a totally different philosophy… They”. There is no “they.”
2) To explain the philosophy I think you were trying to portray as “YU’s”, I think you missed a few important details and nuances. It is not that one needs certain secular studies to be a “complete jew” but rather that certain “secular studies” until relatively recently in history have been one and the same as Torah itself. Therefore they are considered worthwhile studies to ENHANCE one’s avodas Hashem etc. Not “to replace” Torah study.
It is also important to note that there is also a great tolerance of different derachim in YU, so this notion of a uniform “complete jew”, at least from my experiences, is something I don’t think many would subscribe to from there.