Current bandwidth from most ISP's in most countries cannot support decent quality High Definition video.
However, countries like South Korea have 100Mb/s available now, and are rolling out Gigabit connections.
Australia (once the government sorts out the ongoing argument) is rolling out 100Mb/s optical fiber, and is likely to increase that to Gigabit as it develops.
Uncompressed, a 20 minute broadcast would require roughly 4TB of storage.
The only people that use uncompressed video are the content producers. There really is no reason to haul TB's of data across a wide distribution network (at this point in time) for general consumers.
Consider a Bluray - 2Hrs = 25GB -> 1hr = 12.5GB -> 20minutes = 4.17 GB.
That works out as ->12.5GB * 1024*1024 / (60*60) = 3640.889 KB/s ->29127.11 Kb/s (28.444Mb/s)
You can easily haul that across a reliable 100Mb/s link in real time .. assuming a 40% efficiency on a dedicated 100Mb/s link, and that your ISP has enough capacity in the backbone
I'd be hesitant to try it on 24MB/s ADSL2+, or 30Mb/s ... but even this is possible with just a little extra compression ratio (lower quality) and some decent buffering. The extremely low quality that current online HD content is a reflection of the low bandwidth available to most consumers at the moment, and content companies are attempting to maximise their potential customer base.
Broadband is getting better, at least in countries that aren't flat-out penniless, and once a large number of high bandwidth customers are available, content quality will increase.
It's all a matter of time