Yeah, this has been brought up before and nothing seems to really have come of it. As ludicrously huge and descriptive as user agent strings can (and typically are) these days, adding a "Skyfire" to the end wouldn't be a big deal.
Couple of things to consider:
1. Some sites (probably not many) *may* intentionally try to block Skyfire if they decide that you shouldn't be using their content on a mobile device. I don't know if the recent issues with Hulu are along those lines, but it's possible. As a corollary to this, some companies may NEED to block access, legally, because they don't have rights to stream content to mobile. Fox TV may give Hulu rights to stream Rescue Me to desktop PCs, but someone else may have the rights to stream to mobile devices as a completely separate legal deal.
2. Skyfire is meant to be as close to a desktop browser as you can get without being on a desktop. With that in mind, web authors shouldn't have to author specifically for Skyfire so there should be no real need to know if a browser is Skyfire or not. You just know that it's a FF2 based browser and that should be good enough. You can always build something into your site that asks what browser someone is using, let them set it in their profile, let them set their preferred default viewport or whatever else you want to do in order to cater to a smaller screen or whatever.
There are probably other points, but those are the ones that pop to mind immediately.
On a related topic, some light reading:
http://webaim.org/blog/user-agent-string-history/