When our users login to ArcGIS Online, Pro, or other Esri products using an enterprise login (SAML/Shibboleth), they get a generic login page from our identity provider, unlike some other significant service providers, such as Canvas. The first image below shows a generic login screen, the second shows a login screen with information about the service the user is attempting to access, and the third images shows extended information about the service provider.
For enterprise logins using SAML, the identity provider (your organization) should be provided with metadata from the service provider (Esri) to support a more informative login page, allowing the identity provider to render the information as desired.
With SAML, this can be done with <mdui:UIInfo>, described in the SAML V2.0 Metadata Extensions for Login and Discovery User Interface Version 1.0 standard. Esri could provide the elements necessary to support more informative login screens.
As a bonus, allowing ArcGIS Online organizations might be allowed to customize the Description and InformationURL elements.