TLIK: Chasidishe yeshivos or Litvishe yeshivos? There’s a huge difference. You’re correct that the Chasidishe yeshivos aren’t losing their student population in Brooklyn, but the Litvishe chadorim/mesivtas/kollelim very much are. (And from my non-authoritative understanding this is also being experienced by out-of-town Litvishe yeshivos/mesivtas.)
There is unquestionably a very notable migration of newly married couples from all over Litvishe America (as well as to a much lesser extent from outside our borders) to Lakewood and its environs, as well as a slightly less numeric, but also a notable one, of somewhat older couples with yeshiva aged children moving to Lakewood from New York and from out of town. But it is the newly marrieds coming to Lakewood from elsewhere that are the greatest contributers of the dropping Yeshiva population elsewhere where they’d of naturally otherwise had stayed and raised their young and growing families if not for moving as a couple to Lakewood to stay in Kollel there or to purchase affordable housing there (compared to unaffordable housing in Brooklyn and other large metro areas).