Ash – no shaychus. If that was all then there would be no difference to the Yeshivish. DaMoshe but it accurately when he mentioned “the role of the Tzaddik”.
Joseph – agreed. The issue is not that the Rebbe’s son inherits the Chassidus (and all of the property that goes along with it), but that he inherits the Chassidim (who should go to the best qualified Rov, not the son of who used to be most qualified). It also results in minimally qualified people (if that) running the show (and enjoying the monetary benefits) just because their great-grandfather did some good (then again, you see it today with the Yeshivish as well, and the hereditary yerusha of seats on the Moetzes, for example).
DaMoshe – modern Chassidim are nothing close to what the Gaon describes as Chassidus. They too have evolved to be Lomdei Torah, just as the Litvaks have become more Chassidish.