Maybe in 5 years or so, but right now I can't see it taking off!
I would say much longer than that. The government's big target for broadband being a minimum of 2Mbit coverage for the UK, which they are still nowhere near, and this service requires around double that in it's current form, if they improve the quality of the stream that will obviously go up. America's broadband infrastructure is pretty much in the same boat, vast divides in available speeds, some able to get 50Mbit+ connections fine, but a lot struggling on something barely describable as a dial-up.
Easily 10-20 years just before the majority of the people will be able to viably access a service like this, again thats in it's current form, no doubt at some point in the next 10-20 years the quality/bandwidth requirement will have increased. So without a big investment in broadband, particularly in America, these services are going to have an uphill struggle.
This is then leaving out the actual capacity of the networks we connect to, all those currently enjoying 20/50Mbit connections, if those were actually available to even a fraction more people the network capacities would be so saturated that you, nor they, would be getting decent speeds in any measure. Add to that ISPs restrictions, which can be a bit tyrannical today, if a large high bandwidth, constant streaming service took off, before they could have a chance to invest the vast time + finance to increase capacity, they would have to turn it into a despotic drip feed where everyone would be lucky to browse a few youtube videos a month.
All this is a massive shame, because services like these are amazing and could do so much for gaming. But they can't make it big with the current state of broadband and in making it big would cripple networks without super serious investment from private/public sectors, which thus far have shown that in the case of UK/US, just aren't willing to put any serious investment and set their mid-long term plans at rather pitiful upgrades. This plus the economy being in the rather ropey shape it's in, ultrafast broadband I doubt will be making the top of the list in any governments agendas for the foreseeable future.
So they will grow much bigger than they are now, just a shame nowhere near fast or big enough. But will be nice to see how they develop over the next few years. Will just have to hope some kind of broadband revolution occurs within the next decade
