If your feet hurt or are cold and wet you will be miserable and curtail your activities.
Always carry an extra set of shoes.
Sometimes it rains, hard.
After the water logged kite festival that year it took my shoes two days to get dry. There is nothing nastier than putting on a cold soggy pair of shoes to go out and about.
Also, even if your feet don’t get wet and cold it is refreshing to give them a wash and switch to a clean pair after a long day of sight seeing.
A pair of soft wool socks is a really good idea.
For the reason above it is a good idea to always carry one pair of nice wool socks. Arriving back from a torrential downpour experience wash your feet with warm water, dry them thoroughly and put on a pair of wool socks. If you follow this with a glass of half-way decent wine and some dumplings you will recover quickly.
You might not need the socks, but they are light, you can use them to protect fragile things and, if you do get a cold wet foot day, you will be ever-so glad you have them.
Xingfu Rule of Toe
I only travel with shoes I have walked three miles in without hot spots or blisters. There are lots of cute practical shoes available today so there are no excuses. Even if the shoe looks comfy you have to actually walk in them: sometimes they rub here or there, the sole is too soft to protect your feet and I have sometimes had shoes that made my knees hurt because they were too spongy.
This rule is the result of pain: I wore a comfortable but too spongy pair to the Forebidden City the first time I went and crawled on hands and knees around the hotel room that night because I wouldn’t put my feet on the ground they hurt so bad.
Take care of your feet and they will carry you far.