I only had the problem using the web browser to view streamed TV on BT Sport. I have watched 4K videos on Youtube with no problems. I have watched programs, including 4K (Worldcup), using the BBC iPlayer with no problems.
My suspicion is that the streamed TV from BT Sport has metatdata which the Web Browser app does not support and doesn't know what to do with it, so crashes. BBC's iPlayer, Netflix, Now TV and the ITV Hub have apps which support the corresponding channels and presumably will manage any metadata correctly, but there is no app (afaik) for BT Sport.