Cyclocross bikes also have higher bottom brackets
It doesn't matter much anyway and CX bikes from US brands had already started lowering the BB of the CX bikes because US courses designers are usually less keen on putting off cambers section than euro courses designers.
The explanation I heard for the traditionally higher brackets is that it facilitates quicker turning. Is there truth to this or is this more of a marketing thing?
The rest is mostly the ability to pedal in the corners without clipping a wheel, which help maintain and feel grip, tradition and also to help on the many off camber sections the courses used to have.
I think quicker turning has never been the true reason imo.