Not so.
Many of Brooks traditional designs require a traditional seatpin, not a micro-adjust post.
The one Brooks supply with a saddle is crap. Stamped pressed steel of very low quality. It will slip, and then become useless.
They sell an aftermarket one which is better, but that's the best part of £20 on something they should have included for free.
https://www.sjscycles.co.uk/saddles...-clamp-78-inch-222-mm-for-double-rail-byb105/
Very possible, and in fact common.
We could also talk about the number that are built misaligned. Crap quality control.
They were OK for £25. For £125, they are a ripoff.