That is a huge problem with HEVC right now.
The only browser that does support it AFAIK is Edge, and in that case only if you have HEVC hardware acceleration in your system.
From what I understand the lack of browser support is mostly due to licensing issues. FWIW, VP9 has decent software decode support on all current desktop browsers except Safari
Netflix did just announce that they will stream 4K HEVC to Edge and their Windows 10 app - but curiously chose to allow this only for users of Intel's new Kaby Lake CPUs - even though users like myself with an old Sandy Bridge CPU and a new GTX 1080 GPU could play this content perfectly fine... Hmm...
Basically HEVC distribution today is limited to smart TVs, set top boxes, and a few edge cases like Netflix on Kaby Lake on Windows 10.
There may also be some linear TV contribution or distribution being done via satellite using HEVC, but that's also kind of an edge case.
HEVC is fabulous, but until we see broad support on the desktop I think VP9 will be the "current gen" codec of choice for in-browser streaming, but with AVC still being hugely prevalent as well for "non youtube" sites
