In short, because the following works despite quoting and will execute the echos
a=(); x='a[$(echo >&2 what; echo 0)]'; [[ 'x' -eq 0 ]]
> arg1 OP arg2
> OP is one of -eq, -ne, -lt, -le, -gt, or -ge. [...] When used with the [[ command, Arg1 and Arg2 are evaluated as arithmetic expressions (see ARITHMETIC EVALUATION above).
> ARITHMETIC EVALUATION
> Within an expression, shell variables may also be referenced by name without using the parameter expansion syntax.
> The value of a variable is evaluated as an arithmetic expression when it is referenced
> Arrays
> The subscript is treated as an arithmetic expression that must evaluate to a number.
> [[ expression ]]
> The shell performs [...] arithmetic expansion, command substitution [...] on those words.
Given that reading, that both subscripts and values of variables in arithmetic expression are treated as arithmetic expressions, and that command substitution is peformed after arithmetic expansion in `[[`, I kinda expected the following to work:
$ x='$(echo >&2 what; echo 0)'; [[ 0 -eq x ]]
bash: [[: $(echo >&2 what; echo 0): syntax error: operand expected (error token is "$(echo >&2 what; echo 0)")
>> The shell performs [...] arithmetic expansion, command substitution [...] on those words.
> [...] and that command substitution is peformed after arithmetic expansion in `[[` [...]
You're right. That doesn't apply. I was equating "arithmetic expansion" with "evaluation of arithmetic expressions", but I see now the former is specifically about `$(())`.