In what way would it change anything? The "billion dollars mistake" is that because "nothing" is part of every type, any value you get could really be missing, and you have to either hope for the best (and die like the rest) or program ridiculously defensively.
Having a magical sentinel per type would have the exact same issue, namely that "nothing" is part of the type itself, and so you can never be sure at compile time that you do have "something".
That's what opt-in nullability (whether through option types or language builtins or a hybrid) changes, by default if you're told you have an A it can only be a valid A, and if you're told you might have an A you must either check for it or use "missing-safe" operations.
There's already division by zero and NaN to trip you up in IEEE754.