The A size formats are based around A0 being 1m² in area, the B size formats are based around the short edge of B0 being 1m long. The aspect ratio of both A & B sizes are √2.
Lack of demand in the States for ISO 216 sizes in general makes it so that relatively/comparatively few stock such paper in the U.S. When wanting to print to the edges (full bleed), publishers will often print on B sized paper sheets with crop marks for A size (and then crop the paper to A size) or similarly print on A and crop to B.
B5 paper sheets don't seem to be easily available in the UK.
B5 books are the most common size though, most of my school exercise books were B5 or B4 — that allowed me to glue in a sheet of A-sized paper, possibly folded in half.
To answer your question about my preference... For non-fiction books, A4 pages seem too big for me, A5 pages seem little too small to me, and B5 pages seem just right. Again, this is just for non-fiction books. Fiction books I prefer more A5-sized. Just my own personal, subjective preference. That's all.
The strict interpretation of the B series as a packaging format for the A series only seems somewhat archaic.