I don't chamfer the case mouths for .45 ACP.
If you clean brass (using a tumbler) before resizing/depriming, you have nice clean brass running in the die and you knock out any media which might be trapped in the flash hole during depriming.
I have never worried about primer residue.
While those who use a single stage press can create as many "operations" as they like, if you use a progressive press you tend to like stuffing clean brass in the first station and watching finished rounds fall out the last one.
A word of caution about cleaning brass - There are quite a few who like to use Brasso and similar products to make the brass "really shiny". Compounds which contain ammonia do create shiny brass, and also chemically attack the brass and weaken it.
Clean is good. Mirror finish shiny is unnecessary, especially if you use chemicals to accomplish this.
.30-06 Springfield: 100 yrs + and still going strong