There generally has requirements for renaming, appending, removing a column from the input plan.
If the input plan has an equivalence properties, it should be preserved as much as possible when the schema is altered.
However, the current EquivalenceProperties::new_with_schema implementation requires the new schema and the original schema being aligned. Specifically, the number of columns and column positions should be consistent. This constraint disallows us to consistently update the equivalence properties when the schema is altered.
I wonder if we can remove the align constraint.