You are not wrong! An entire subclass of anomaly detection can basically be reduced to: forecast the next data point and then measure the forecast error when the data point arrives.
Well it doesn’t really require a forecast - variance based anomaly detection doesn’t make an assertion of the next point but that its maximum change is within some band. Such models usually can’t be used to make a forecast other than the banding bounds.
That would be a different subclass of anomaly detection solutions.