Need or not need...a bigger issue is simply the technical reality of what you have now. If your non-trivial infrastructure doesn’t have great http2 support, it might be a pretty big lift to make that change first.
Yes, it is such a foundational thing that it has to be woven into how you run your infrastructure. Can't just drop it in in most cases. If my memory serves me well, Google basically re-started their entire codebase/infra from scratch - google3 (version 2 was skipped, apparently) to accommodate this shift.