I've come to the conclusion that I like stiffer soled shoes for biking.
I have an old pair of 1980s Cannondale touring shoes- the soles themselves are very stiff, like rigid stiff. Not comfortable to walk in- but they look like regular 1980s tennis shoes.
EXACTLY like these, box and everything:
That being said, if I ever get the time/ability/opportunity to do my cross-America bicycle tour- this is what I'll be wearing: