1. What Hetter is there, in Shas or Poskim, for Yeshiva Bochurim to not daven a proper Chazaras HaShatz by Mincha? Now even if you’ll Taanah that back in Slabodka (where I think this minhag originated) they lived Toraso Umnaso, how does this apply in the US, where you have breaks for lunch and breakfast, and in some Yeshivas for Limmudei Chol. I find it hard to believe that you can’t find 5 minutes in a day to do a Chazaras Hashatz like the Chachamim decreed.
R’ Yaakov Kamenetzky is quoted as saying that the original takana to say chazaras hasha”tz was not made in a beis medrash, where the attendees generally know how to daven themselves. It was only made for shuls, where it is common to have people who need to be yotzei with the sha”tz.
Shacharis is different because of s’michas geulah lit’filah (at least according to the common minhag of starting t’filas lachash after kedusha).
You also don’t lose Birchas Kohanim at Mincha (I’m not sure if R’ Yaakov said this point).