HTTP/2 provides performance and parallelization improvements over HTTP/1.1, notably solving the head-of-line blocking problem. This is particularly important when loading minified javascript modules, such as the web map viewer.
Although HTTP/2 effectively requires TLS, the default Enterprise setup uses TLS on ports 7443 and 6443 so this requirement isn't above what is already a default (and good practice).
Apache Tomcat has supported HTTP/2 since version 8.5; version 9 was included with ArcGIS Server 11.2, so this should be stable and may be as simple as a configuration change. From my testing by editing the tomcat server.xml for both Server and Portal at Enterprise 11.5 on Windows, this does seem to just be that easy.
