In order to satisfy both the field viewers and the webcast viewers, FIRST would probably have to double its investment in video hardware. They'd need the whole pipeline of camera->mixer->webcaster for both the wide-field camera destined for the webcast and the close-in/interesting stuff destined for the back of the field.
You guys have to remember though: at a regional, there are probably going to be 40 teams, and at least 10 people from each team sitting at the field, watching. How many webcast viewers are there (I don't know, but I imagine it is less than 400)? How many people stand in front of the screens in front of the pit trying to see the match? Probably less than 10, continuously.
I think the best thing to do would be for one team to record the full field of each match with a high definition camcorder and distribute the videos afterwards via bittorrent. There are camcorders available within a team's budget, like this
Sony 1080p model that records to a hard drive for $1800CDN. For a less crazy price,
here is another one that does 1440x1080 (not real 1080p, but still very good) for $1200. My boss has the $1800 one and says he loves it, perhaps I can borrow it for the waterloo regional next year.