I have only packed an extra pair of shoes once, on my RS tour. I used them once…only because I packed them, better use them. (This is the same trip I only packed one extra pair of pants and destroyed one of my two pairs the day before the tour…I did have a lovely interaction with Greek ladies as a result though. I digress.) So ordinarily I would say one pair of shoes (and now 3 pairs of slacks, LOL); however, if you are on a formal tour and might not be in places to shop or have time to shop, or you have problematic feet, it might be a good idea to bring a light, well loved, extra pair of shoes. We each have different physical requirements to which we should pay attention and pack accordingly. There is one item that packing lists suggest packing one of, but I pack 3 or 4 because, generally, I could not find this item easily in Europe…IMO. So, you do you! Follow your gut.
Hold harmless, I do pack cheap, thin flip flops for the shower and hotel room, but I don’t consider them shoes as I couldn’t walk in them.
PS, I have never had wet shoes that weren’t dry by morning, but if it is an extremely torrential day, just put an extra pair of socks in your day bag/purse.