I recently had rodent damage and had to replace most of the parts in the AC system, adjuster from Geico visited the shop in a few days and the check from Geico arrived in about a week. Car shop (Toyota Berkeley) said it sometimes takes 2 weeks for the insurance check to arrive. And Geico paid for car rental (5 days worth) YMMV but my experience with Geico was not as annoying as yours with Allstate.
Geico
YMMV but my experience with Geico was not as annoying as yours with Allstate.