I'd like to think that the Internet is prepared to handle streaming 1080p video, but as you mentioned, Austin, there are still big bandwidth concerns, no matter how fast we can stream.
1) ISPs are still unwilling to give decent upload rates to most of their customers, meaning that only the most dedicated uploaders will be willing to share 1080p videos. The rest won't bother because of the insanely long upload time (which, by the way, will kill their internet speed until it's finished uploading).
2) Most ISP services don't offer enough bandwidth to make regular viewing of 1080p streaming videos viable. I only get 60GB a month of download bandwidth. That's not much more than a couple of blu-ray quality movies. It's never been a problem, but if, for example, every video on Youtube was 1080p, it could quickly become a problem.
On the other side:
1080p monitors for computers are becoming more standard on new systems. Looking at 22 inch monitors here, the majority of them tend to be 1080p now, not 1680x1050 like they were when I bought mine. Also, the price of a 22" 1080p monitor isn't much more than a 19" so it's becoming a viable upgrade option.
In short: I think they should have stuck with 720p if they wanted to push for more HD content. 1080p isn't quite feasible as a streaming format in a lot of cases: there is a reason that no TV broadcaster in Canada is broadcasting 1080p on digital cable yet! It's all 1080i and 720p because the bandwidth just isn't there. I think it's the same with the internet.
Sure, we can start establishing it but the internet just isn't ready to handle 1080p as the mainstream format for streaming video. Upload times are going to be brutal, discouraging people from using the format for now. The majority of people don't have 1080p monitors yet, but this will be changing quite a bit in the next year or two, I imagine.
Establish 720p as a standard and give ISPs and monitors a chance to catch up.