Spotfire Web Player: Why do I only see 3 connector options when initiating a data connection in Web Player?

When trying to create a connection using a connector in Web Player, only 3 options are shown:

However when trying to create a connection using a connector in Analyst client shows many more options:

As of this article's writing, the only connectors that can be created in Web Player are 'Google Analytics', 'Google Analytics (Universal Analytics)', and 'Salesforce'. The remaining connectors must have the initial connection set up in the Analyst client - the connection can then be used by end-users to retrieve data in the Web Player. 

This Spotfire documentation page describes this limitation:

https://docs.tibco.com/pub/sfire-analyst/14.0.0/doc/html/en-US/TIB_sfire_client/client/topics/en-US/acc_data_in_databases.html

This Spotfire documentation page describes the Web Player configuration for the connectors to be used in Web Player:
https://docs.tibco.com/pub/spotfire_server/14.0.0/doc/html/TIB_sfire_server_tsas_admin_help/server/topics/configuring_connectors_for_use_with_web_clients_and_spotfire_automation_services.html