The biggest impact you can have on your users experience is to trim down the number of connections and the size of your pages. Long after that you can start worrying about round-trip-times to the server. This blog post is a nice example: 30 requests (ublock origin blocked another 12, with those enabled the time to load increases to a whopping 28 seconds), 2.5M transferred, 7 seconds load time. And all that for 4K pay…
Number of connections isn't that relevant with HTTP2
The number of connections to one host isn't relevant in HTTP2. As ublock is blocking some ~20 connections these are going to different hosts. Connecting to a different host in HTTP2 is no different then HTTP1.1
If your HTTP2 is terminating at MANY boxes within your infrastructure you are failing to understand how HTTP2 works. Connections within a single TLS/TCP/IP connection are free, new TLS/TCP/IP connections cost exactly as much as before.