A great number of Alaskans are dependent upon government handouts. That's why Murkowski keeps winning. She brings home the $$$.
Alaska is a right of center, very Republican state, but not really that conservative overall.
Murkwoski is left of center and you can get a more conservative Senator than her elected there...but a full throated conservative would likely not win there. Dan Sullivan is more in the mold of an Alaska Republican that can win and still be right of center in overall philosophy.