Not only do heels modify someone's height, they also modify the range of motion for doing something like squatting down.
For kids this isn't a problem, they can squat all the way down without issue. But as an adult, regaining that lost mobility is a process!
But, try this: elevate your heels by an inch. Then try 2 inches. You'll find that you can more comfortably squat down the more your heels are elevated. It also impacts center of balance and the angles at which your back is at while squatting.
I read once that people in a certain country were accustomed to doing work in a squat position, perhaps due to lack of chairs/seats for the poor, but I thought it was cool after being forced into a chair/desk posture for my entire life. I've also heard that catchers in baseball retire because their knees give out after the constant squat/crouch position, catching pitches at home plate. Should catchers wear high heels? Got to watch "A League of Their Own" again...
There are also wedges/slant boards for this purpose.
Lifters also have another purpose: they provide stability by connecting your feet more "solidly" to the ground. Other gym shoes (cross-trainers, running shoes) have padding in them... which is awesome for running but that squishiness can translate to instability when you're literally doubling or tripling the amount of weight.
Consequently, some lifters who have the ankle mobility will lift without shoes. Given the state of most gym floors, that's a no from me, dawg, but hey to each their own.
For kids this isn't a problem, they can squat all the way down without issue. But as an adult, regaining that lost mobility is a process!
But, try this: elevate your heels by an inch. Then try 2 inches. You'll find that you can more comfortably squat down the more your heels are elevated. It also impacts center of balance and the angles at which your back is at while squatting.