Why can't indexed views have a MAX() aggregate?

These aggregates are not allowed because they cannot be recomputed solely based on the changed values.

Some aggregates, like COUNT_BIG() or SUM(), can be recomputed just by looking at the data that changed. These are allowed within an indexed view because, if an underlying value changes, the impact of that change can be directly calculated.

Other aggregates, like MIN() and MAX(), cannot be recomputed just by looking at the data that is being changed. If you delete the value that is currently the max or min, then the new max or min has to be searched for and found in the entire table.

The same principle applies to other aggregates, like AVG() or the standard variation aggregates. SQL cannot recompute them just from the values changed, but needs to re-scan the entire table to get the new value.