I for one would probably use such a LinkedIn app, and I guess it would pretty quickly get up to a few hundred or few thousand users. So in principle I don't think that's such a bad idea.
However, I have two doubts.
SO owners probably are not interested enough.
The problem lies in that LinkedIn only
offers their API to "approved LinkedIn
partners", so, and I may be wrong
here, the request may have to come
from SO/SF itself as opposed to
I think you are correct about this. Personally I'd guess that Jeff et al wouldn't be very interested at all in creating a LinkedIn app - they probably find there are way more urgent things to be working on in the SOFU sites themselves. So at the very least someone from Stackoverflow.com LLC would need to officially sanction the app, even if it was actually created by interested users.
More importantly, LinkedIn seems to be very selective about the 3rd party apps. I mean, look at their app directory - there are currently only ten (10) applications available.
Quote from their FAQ:
API access is only offered to approved
LinkedIn partners. We partner with
companies who provide clearly
compelling value to our users,
generally giving priority to
integrations that provide the most
value to the greatest number of
Reading that makes it pretty clear to me that they wouldn't want an app that's aimed at so small a portion of their users and does so little (show a rep score and provide a link is pretty minimalistic after all). So while there are lots of (technical) software and IT people on LinkedIn, in the bigger scheme of things they are a tiny minority there. Note that none of the current 3rd party apps are limited to some specific field or industry.
So, in conclusion, simply linking to your SOFU user page from your LinkedIn profile will probably remain the best / only option for some time. =)
Update (2014): For what it's worth, I recently started using the method described in this answer for highlighting Stack Overflow profile in the Summary section of my LinkedIn profile, using flair. Not perfect, but kinda ok.