Streaming nowadays doesn't just mean watching on a small screen. Netflix, Amazon Prime etc will become ever popular and these apps are built in to TVs now. I even a 'Netflix' button on my TV remote!
The biggest problem will be fragmentation and cost and will turn a lot of sport into 'niches' with much less viewers who all pay a premium. If you want to watch sport A & B then then you need a certain package, but for sport A, B & C then another package is required on top of the one you already have. Other channnels (BT Sport for example) can only be received if you have certain packages with BT/SKY/Talk talk etc. I will soon have a 1000meg mega fast connection but because a BT line copper connection will only give 1 meg if I'm lucky, I can't use any big provider who do package bundles so if i wanted BT Sport via streaming, I can't get it (so i understand anyway).
Its obvious why illegal streams are so popular.
Everything is getting broken up now and theres too much cost involved. Couple that with minimum 1 year or more contracts, it makes it harder to swap and change.
Right now we have Sky (without Sky Sports) and get the F1 channel free as we're an old legacy customer but after 25+ years of being an F1 fan who never missed a practise/qualy/pre race/race/ and all the afters up until the BBC/Sky split, I'm cancelling my Sky account and just using Freeview and Netflix.
Its just not worth the money anymore paying Sky with dull races, adverts and predictable results pretty much every race.
Even if the races improved, F1 - and other sports - needs an option of streaming races direct where I don't need to pay for a particular package that I can't get or don't have. I just to want to pay a non extortionate price direct from the F1 website and be able to stream the race on any device which I can hook up to my TV easily.