why does the thickness of the sole matter? don't want to assume you want a stiffer sole. but a stiffer sole doesn't have to be thicker
thicker is a feature
stuffer is a benefit
it might help if we knew what benefit you were looking for
for example, I was just thinking about how I started with smooth bottomed cycling shoes, but w/o cleats. these have more rigid soles. those worked out really well for me. I imagine they would work real well w/ traditional toe clips aka cages