I am surprised by what is missing from the discussion.
1) If we look on our Gedolei Yisroel, both present and the history of the past several generations, whether Litvish or Chassidish, there was a concept of vacation. There were several locations around Europe where Chassidishe rebbes congregated during the summer. Our biographies are full of encounters when this one met that one. The idea of taking time off for rest and leisure is not about bitul Torah, but about taking leave from the rigors of the daily routine. Lehavdil, sports also have seasons that occupy part of the year, where the rest of the year can be used for other aspects of life. We have our own role models, and they disprove the bitul Torah argument.
2) The issue that there is vacation is not worthy of debate. Try managing without any interruption of grueling daily routine. What presents a problem is that this is placed on the academic calendar. Not all talmidim, talmidos, hanhala, etc. are ready for such vacation at the same time. An ill scheduled vacation is apt to lose much of the potential benefit. Similar to the belief that the curriculum is appropriate for each talmid, and that the talmid must adapt to that curriculum, so to is the schedule for vacation. Neither of these is true, and pushing a square peg into a round hole is something that even babies discover cannot be done (at least according to Fisher-Price). This not an issue of Torah hashkafah. It is about common sense.