I use clips and straps with no cleats and must have foot retention because of nerve damage in my back that affects my left leg and foot... without this my foot will often slip out of position or lift off the pedal as the motor nerves are affected. I like to be able to get off my bike and walk and cleats or straight up clipless road shoes hamper my walking ability.

My right leg sometimes does nearly 100% of the work and with the right shoes cinched down snugly I can still pedal very efficiently without my feet slipping out the back... my left foot gets locked in first as I cannot always feel the pedal.

Adidas Stan Smith tennis shoes are my preferred shoe and have been for 20 years... the hold quite well and don't slip and I have some Uvex shoes which have also been quite decent... these are also leather with a nice shape for clips and straps.

I also use clipless pedals which are better when I am dead legging it and have an ever growing collection of shoes and pedals... clipless mtb and touring / commuting shoes are my favourites as they are comfortable enough to stand and work in and I also have straight up road pedals for long road rides where there will be no off the bike time.

Riding fixed also makes me more efficient as sometimes my left leg just needs to go for a ride and after some time it will usually wake up a little and do a little more work.

Anyways... I have been doing one legged drills for a few years now and can still spin things like a gerbil on crack and have not blown out of a clip yet... part of that also stems from knowing how to pedal efficiently... this is something many cyclists do not do.