I have used crates but never for housetraining (mine have been used for all sorts of things, including keeping the kittens confined at night, a cat with a catheter in, a dog who has SA if am upstairs so she now sleeps in a crate upstairs so cats still have their haven and keep their food, confining pups when am out and sometimes overnight, sick dogs and so on)
I never stick rigidly to time re housetraining, i.e., letting them out every hour on the hour sort of thing but tend to use 'moments' in the day, e.g. after they wake up, before they eat, after they eat, before/after play/training, etc. and it seems to work. If they do have accidents then so be it I find we get there in the end relatively easily regardless of accidents in the house and all pups will take as short or as long as they do - some pups longer than you expect and some yippee it works quickly.
I find with this method am more relaxed and so the pup I have usually is too