Stale Statistics and View performance on SQL Server 2016
What could be the reason that even with Auto Update Statistics enabled and level 130, the statistics are stale?


Automatic statistic updates are not enough
You should be proactively updating statistics  (more often than Auto Update Stats does) with FULLSCAN, to get better cardinality estimations and better query execution plans.
For more info watch this (Brent talks statistics sometime later in the video):
https://www.brentozar.com/training/think-like-sql-server-engine/


Is it advisable (or a good idea) to have a utility job every night, post nightly ETL batch completion to update the statistics of all tables?


Yes, update statistics with FULLSCAN for tables affected by the ETL batch processing