Do you still need both the 32 bit and 64 bit connectors installed for SSIS 2016?
In the case of DBMSs that only offer ODBC connectors to interface with SSIS (Among other things) the answer is that only the 32-bit connector needs to be installed to make an ODBC data source that SSIS 2016 can recognize. For my environment this was the case with IBM Informix and Progress OpenEdge.

In the case of Oracle the prevailing wisdom I read back when I was working with SSIS 2012 still applies. I had to install both the 32 and 64 bit instant clients, configure symbolic links so that Windows could leverage both of them as it needed, and make the appropriate TNS files and environment variables for the Oracle connector to function.

MySQL worked with just the most recent, 64-bit .NET connector. The same applied to Teradata. It seems that only ODBC connectors and Oracle need 32-bit access.