Parsing further, however, "stops the cluster period" doesn't necessarily mean ends the cluster period. It could just mean stops it temporarily, which is not uncommon though maybe even that doesn't happen "often" based on the definition provided.
It just so happens that the very "world's leading CH expert" that I mentioned, Dr. Goadsby, did a double-blind etc. etc. study of the effectiveness of the recommended prednisone taper. You can read about it here. https://www.jwatch.org/na52979/2021/01/05/prednisone-transitional-treatment-episodic-cluster
Having read that, you can explain to me what the heck it means. It mentions some people "achieving attack freedom by 7 days," but not how many, and not whether anyone's cluster period was completely ended. Overall it seems (to me) that maybe most people got significant reductions in attacks but not complete freedom from attacks. Being able to read the whole thing and not just a synopsis would probably help.
And then there's this one, with a few hundred authors, that also says (I think) that pred reduced attacks but says nothing about eliminating them in the short run or fully ending the cycle. https://pubmed.ncbi.nlm.nih.gov/33245858/ Although I see here again, in this discussion of this study (https://www.reliasmedia.com/articles/147514-prednisone-vs-placebo-in-short-term-prevention-of-episodic-cluster-headaches), the unclear statement "After seven days, cluster attacks had ceased in 35% of the prednisone group." -- which of course still fails to meet the provided description of "often," and still doesn't tell us whether that cessation was temporary or cycle-ending.
But I do remember, as others might, a crabby woman who wanted to take pred while she was pregnant and asked whether it would end her cycle. She was told "might stop it temporarily but probably not end it," which was very irritating to her. She mustered the energy just a few days later to tell us we were idiots because it did end her cycle, long before she could possibly have known whether her cycle had ended or not. But I am nonetheless adding her to jon''s instance and declaring that to be often.