I think the big switch will happen once most people have TV's that can do 10bit color and true HDR. H264 can definitely do 10 bit but I'm not sure how well it handles higher dynamic range content (or if it even can) but H265 definitely can.
I feel like the switch from AVC (h.264) to HEVC (h.265) has already happened. It's used in 4k blu rays, most premium streaming services, and hardware support has been ubiquitous for at least 6 years.
