How I’ve deliberated over this topic but with more of an emphasis on waterproof-ness!
There’s little if nothing out there that will provide a flat, stiff-ish, grippy sole and a GORE-TEX or eVENT membrane in a low-rise boot. I’ve searched and searched, the nearest I’ve seen are Mephisto Muto – French, semi-casual and expensive leather faux-walking boot, Clarks Rockrider GTX (similar to Muto but cheaper), Nike Blazer mid GTX (can’t find anywhere selling ’em) and some others the name of which escapes me in one of the outdoors shops on Deansgate, Manchester. I use AM40s and while they are great in dry and damp conditions, in the wet they only serve as foot-sponges. 5 10s are even soggier and take longer to dry by all accounts.
Most approach shoes and mid-height trail boots have a cleated sole with a pronounced instep which kills the grip of flat pedals and limits one’s foot placement on the pedal.
There’s a gap in the market here I reckon.