I always found it fascinating this seems to purposefully (accidentally?) prohibit employees of big companies who are prohibited from open source software development work without jumping through a lot of hoops.
Not purposefully, and a link to code projects isn't needed; users are welcome to invite based on their own criteria. A lot of people have been invited from the chat room just for describing an insightful comment they'd like to post, or by idling and chatting for a while.
My least favorite thing about the invite system is that it's a bigger hurdle to new developers who have a smaller professional network, have few or no public code repos, and have the least confidence to speak up in an unfamiliar social situation like the chat room. We previously had a formal invite request system to encourage them but had to turn it off when spammers outnumbered the newbies (it's still there behind a feature toggle for the sister sites using the codebase). Open signups would be much worse for spam, eternal September, sockpuppets, etc. If you (or anyone!) has suggestions for addressing this problem, I'd appreciate hearing your thoughts (email in profile, or #lobsters on Freenode).
If your company doesn't let you put up dotfiles, or blog about some neat framework trick you learned, I'd be shocked.
Folks that don't have the time/inclination to display those things frankly probably aren't going to have the time/inclination to contribute meaningfully to the community, and the accumulation of a nonparticipating majority is one of the pathologies of these sorts of forums.