You're correct that the reason we have invites is so that we only have legitimate programmers on the site.
As for why you should, you've already answered this question in your first line - it's "a nice thing". You invite other people to join Careers because you want to help them get a better job. This is a nice thing to do to help your fellow programmers.
It's the same reason a lot of people post answers on Stack Overflow - because they want to help.
I see you yourself have answered some 161 questions on Stack Overflow. Using your own logic, you have given away valuable knowledge that might help other programmers proceed in their own careers! What if they were completely identical to you apart from that one piece of information - now if you're both applying for the same job, you've thrown away that one tiny advantage!
Fortunately, helping people out makes you a stronger candidate for jobs, not a weaker one. You can really improve your profile by spending time helping out your fellow programmers any way you can - through answering Stack Overflow questions, building open source etc. If you invite someone to Careers and they land a great job, who knows how they might repay the favour?
Be nice to people, help others out and the rewards will follow.
This is a far better strategy than trying to keep Stack Overflow Careers a secret.