Why can't the mapping field be deleted？
Elasticsearch allows fields to be added and some mappings to be changed but deleting fields from a mapping is not allowed. This restriction has as far as I know always been in place, so you will need to reindex to remove the field from the mapping.
If I reindex, is the index after reindex consistent with the original one?
Reindex is based on a snapshot of the data when the reindex operation starts so if you continue to index or update the source index while you reindex those documents will not be covered.