It’s not quite; HTTP/2 is not in fact uniformly superior to HTTP/1.1. Search around and you’ll find the reasons; all I’ll mention here is the two biggest keywords: WebSockets and head-of-line blocking.

The end result is that HTTP/2 is an improvement for most common workloads, but not all; especially in app-type scenarios with lots of mobile users with suboptimal connections and comparatively few requests (e.g. because you already do batching rather than sending zillions of requests), HTTP/2 can regress typical performance.

WebSockets over HTTP/2 is now specified in RFC 8441; not sure what the implementation status of that is. That solves one of the main problems.

My understanding is that HTTP/3 (with UDP-based QUIC instead of TCP) then resolves all remaining known systemic regressions between HTTP/1.1 and HTTP/2. So yeah, HTTP/1.1 to HTTP/3 should be pretty close to “free speed”.

But even then, it changes performance and load characteristics, and requires the appropriate software support, and that means that many users will need to be very careful about the upgrade, so that they don’t break things. So it’s not quite free after all.