You're labeling as a fact that Dolfamingo is closer to Katakuri than Cracker yet Big Mom (who especially at that time in the story was getting wanked by Oda for her information network) sent Cracker to handle Luffy with Intel of Dolfamingo's defeat
I don't think it makes much sense for Doffy to be at the bottom of commander tier when it was implied multiple times that admirals would be sent if the WG wanted to capture him.