A lot of standing on a hard floor can cause some pain in feet, legs or back, for some people, but I doubt you stand enough for it to matter.i would not think twice about it at homes.
In retail stores, if the floors are hard, carpets and matts are at the register to help cashiers who stand all day on an othersie very hard service. Department store use carpet typically in the main merchandise areas, even though the aisles are hard surfaces, not only for decor reasons, but alos to help the sales people who stand all day.
Some cultures feel not wearing some sort of “shoe” is less sanitary or impolite. Many Americans kick off their shoes even with guests in the house, walk bare foot or stocking/sock foot. Many Latin American cultures would find it lacking class or improper. The Japanese require you remove your shoes at the door.
There might be some old wives tale mixed in with your dad just thinks you should in his suggestion.
My brother-in-law thinks it is less sanitary to walk barefoot at home. But, the truth is people who wear their outside shoes in the house, have much germier floors. So, he would need to change to inside shoes right at the door to be correct, but he doesn’t.