8÷2(2+2) is designed to be ambiguous. Arguing over what the correct reading is, is futile. There isn't one.
There are, however, instances where determining how it is evaluated are not futile. The ambiguity of presenting the expression to a group of people and asking them to evaluate it is based on their understanding, choice, and memory of what rules to apply.
Present the same expression to a system designed to evaluate numerical or algebraic expressions, and the result will be consistent based on the rules the programmers chose to follow.
Wolfram parses 8÷2(2+2) as (8/2)*(2+2) and returns 16. Excel evaluates =8/2*(2+2) as 16. These systems don't throw up their hands and say "there's not an answer", they return one. It behooves the user to understand the rationale behind which answer. It may seem silly and trivial when using single digits, and the dictum to "just put parentheses around everything" an obvious solution. But when the single digits are replaced by variables, and the expression becomes a concatenation of longer parts, where placement of parentheses may not be obvious, knowing how your system is going to evaluate an expression is not futile.