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Work out shoes like chucks etc.
I get how you can lift more because it has a firm heel and the sole that doesnt cushion like a running shoe. But does it really benefit your strength or anything of value.
Just because you can lift more doesnt mean it makes you stronger. So is the push for workout shoes simply so that you get personal bests?
No. The push for "workout shoes" is so you can effectively transfer all of your strength to the floor without an inherently unstable surface disrupting this kinetic chain. Additionally, since running/crosstraining shoes are unstable and do not transfer force efficiently, they can cause increased rates of injury due to failing lifts or forcing people into bad form patterns as a result.
So no. They are not for "personal best" records. It's just stupid to squat on an unstable surface, much like you wouldn't try moving a couch into a living room while pillows were strapped to your feet.