There are many talmidim who do keep a strong kesher to their rebbeim from younger b”m years, but I suppose not to the same degree as CC talmidim.
Of course, a kesher with a rebbi is very important. And definitely 2 years of shimush and limud is enough to pick up the rebbi’s mesorah, so much so that you’ll want to leave and go learn somewhere else.
If BMG isn’t teaching a mesorah, as you claim, then Rav Kotler’s yeshiva is also dead. v’chaval al d’avdin.