associative array initialization via string and without declare

I want to have a global associative array, that is filled at several locations and I can not get it to work to initialize the array with the content of a string without using the declare -A -g over and over at said locations(which I don't feel like is the smartest approach). I've extracted the issue to the code below:

#!/bin/bash

declare -A arr
declare inputString

inputString="([key]=val)"

arr="$inputString"
printf "from variable: ${arr[*]}\n"
printf "from variable: ${arr[key]}\n"

arr=([key]=val)
printf "inline: ${arr[*]}\n"
printf "inline: ${arr[key]}\n"

declare -A arr=$inputString
printf "with declare: ${arr[*]}\n"
printf "with declare: ${arr[key]}\n"

the output is:

from variable: ([key]=val)
from variable: 
inline: val
inline: val
with declare: val
with declare: val

whereas I would expect it to be:

from variable: val
from variable: val
inline: val
inline: val
with declare: val
with declare: val

what do I have to do to accomplish this task?

One bash 4.3+ approach using a nameref:

myadd() {                             # $1 == array name; $2 == key name; $3 == value
    declare -n _arr="$1"              # nameref
    _arr+=(["$2"]="$3")
}

myclear() {
    declare -n _arr="$1"
    _arr=()
}

Taking for a test drive:

unset      arr1 arr2
declare -A arr1 arr2

myadd arr1 keyX 3
myadd arr1 Index_45 16
myadd arr2 long_string_abc long_value_xyz

typeset -p arr1 arr2
    ==> declare -A arr1=([keyX]="3" [Index_45]="16" )
    ==> declare -A arr2=([long_string_abc]="long_value_xyz" )

myclear arr1

myadd arr1 aaa 111
myadd arr1 bbb 222

typeset -p arr1
    ==> declare -A arr1=([bbb]="222" [aaa]="111" )