Interesting timing of this post — shortly before the puzzle with agonies/agonise (common and rare respectively, like monopolies and monopolise) and analogies/analogise (both common)! (Thus, I held off responding until after that puzzle had closed.)
I wondered if some of the apparent inconsistency is a result of the Oxford versus British spelling, so I checked the OED: it prefers monopolize, agonize, and analogize — trashed that theory!
ISTM the -ise ending should be extremely well known to players. On balance, I'd prefer to see all words which can be spelt with either the -ise or -ize ending be treated the same.
