DBCC CHECKDB on Always On databases Do we really need to run DBCC checkdb on a database configured with Always On synchronous updates?

I believe the automatic page repair mechanism should identify the corruption and repair it automatically.
Yes you really need to run checkdb on ALL the secondary replicas. If you read MS document on Automatic Page repair it says

Automatic page repair cannot repair the following control page types:
File header page (page ID 0).
Page 9 (the database boot page).
Allocation pages: Global Allocation Map (GAM) pages, Shared Global Allocation Map (SGAM) pages, and Page Free Space (PFS) pages.

So you can see not all types of repairs are fixed by automatic page repair. What if you encounter corruption not coming under error fixed by automatic repair.
If you are using availability groups on WSFC without FCI the storage would be local storage so you need to separately run checkdb and analyze storage for each replica.