We have a BigQuery Materialized View with:
BI Engine docs clearly state materialized views are supported and we're in line with the limitations. While the docs are a little inconsistent around join support (MV docs say left joins aren't supported, but this Google blog says they are) this MV is allowed to be created with non-incremental option. I've waited at least an hour for any BI Engine config changes to settle.
However, when adding the MV as a Looker Studio data source and then exploring or using in a Looker Report, the BI Engine is not working for this materialized view.