There actually are workarounds to allow mobile support for reports in the Power BI Report Server. While out of the box Power BI Report Server does not support mobile-friendly viewing like Power BI Service, the following can be adopted:
Customise Reports for Mobile Viewing
Develop reports designed specifically for mobile-friendly layouts by optimizing their visuals for much smaller screens. Use the "Custom Layout" functionality in Power BI Desktop to create a version that is defined for mobile devices. Although there is no mobile application for Report Server, this will ensure improved usability over browsers.
Embed Reports in a Mobile-Friendly Web Portal
People will be able to view their Power BI Reports from an internal mobile-optimized web portal. There is also the option of embedding those report URLs within an internal company website or app that employees can access through their mobile devices. Microsoft Sharepoint is effectively tailored to be an internal public domain for hosting or custom HTML portals.
Third-Party Tools
Look for third-party solutions, such as "Mobilizer for Power BI," which help set up mobile viewing for Power BI reports. Typically, these tools allow connecting securely to one's Report Server while providing a user-friendly environment for devices.
They would not give a seamless integrated solution like Power BI Service, but they are good enough to close the gap.