Why bash can't change global array/variable when $() or ` ` is used?

Question

When $() or `` is used bash can't overwrite it.

Here is the code:

#!/usr/bin/env bash

multiply() {
    it=0
    for i in ${arr[*]}; do
        arr[$it]=$((i * 2)) # change the global array
        it=$[ $it + 1 ]
    done

    echo ${arr[*]}
}

arr=(1 2 3 4 5 6 7 8 9 10)
new_arr=($(multiply))

echo "Before: " ${arr[*]}
echo "After:  " ${new_arr[*]}

output:

Before:  1 2 3 4 5 6 7 8 9 10
After:   2 4 6 8 10 12 14 16 18 20

Why it works like that? Aren't the just supposed to assign output to array/variable?