Working out barefoot can help you better feel how your weight is being
displaced on your feet.
My favorite lifting shoes were Chuck Taylors because they are really flat and I can feel the ground better than other shoes with a lot of cushioning.
Running sneakers are not ideal for weight lifting they have too much cushion which will cause slight shifting left and right when you're lifting heavyweight. The shifting reduces the amount of force you can drive into the ground.
If clients don't have any feet issues suggest for them to get some Chuck Taylors, they are lightweight, cheap and are great for strength training at the gym.
Trainers love their workout gear especially their shoes, How many workout shoes do you have?