There was a time, not so long ago in a world where toe strap style pedals were the only option to keeping your feet attached to the bike. In that unenlightened time there were many shoes supplied by cycling stores that did not have cleats or the option of cleats, these shoes were in many cases called touring shoes and were styled to look like normal shoes or trainers. Indeed I had many pairs of these shoes and wore them on an off the bike with no discomfort.
I have spent a couple of weekends looking for some trainers for my beloved who is not yet ready for toe straps yet alone clip-ins. In the end I found some in Sports Direct that fitted the bill, The main thing to look for is a good stiff (as possible) sole a reasonably smooth 'tread pattern' on the sole to ease the process of sliding the foot into and out of the pedal and preferably a double layer on the outside of the shoe where the strap will grip to spread the pressure. This was the basis of a standard cycling shoe before the clip-ins took over the world.