You guys are too hard on this web browser thing. This is not a "convergence" of products. This is first and foremost a gaming machine, with a browser designed for it by a company (Opera) who has attempted to make its negligible impact through browsers designed for portable devices. It's what they do, and it works here.
That said, the weather and internet channels are not meant for extensive use. They're meant for about 5-10 minutes of use. At least that's the way I see it. I think I remember a Nintendo exec saying that these additional channels are intended to make the Wii a sort of quick portal to useful information. So in the morning, you can check the weather and read the paper online, and be out the door in a couple minutes.
That said, the internet channel is a "free trial." Would I pay for it if/when they set a price? Probably not. I'm sure they'll set the price too high if they did, and I can't see anyone paying a lot for a basic web browser.
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Matt