Does ArcGIS Desktop require Internet Explorer?

Answer

Microsoft announced that Internet Explorer 11 would be the product's final release and that it will begin ending support for IE 11 in specific operating systems in June 2022. Microsoft Lifecycle FAQ - Internet Explorer and Microsoft Edge.

The Microsoft Windows Operating System (OS) includes Internet Explorer (IE), and the ArcGIS Desktop requirement is not specifically on IE but the OS.  We recommend you ensure that your Desktop implementations are installed on a supported OS as specified in the Desktop system requirements.

The statement above is valid for all versions of ArcGIS Desktop. Esri has updated documentation for versions of ArcGIS Desktop in General Availability and Extended phases of the product life cycle. Documentation for versions 10.5 and below has been archived and is no longer updated.