For temps > 60F, my solution is Keen bike sandals & thin synthetic socks & let it pour. Both dry quickly.

For colder days, solution is taking the day off the bike. Maybe plastic bags over the socks inside the sandals if I get caught in rain. I do have some neoprene booties that I could fit into the Keen's over wool socks, but I'm just not into cold wet rides.

For commuting, I carry dry socks in the pannier and keep shoes at my office.