The Internet is not some monolithic entity, and there’s certainly not a culture that defines the Internet. If there was, it would probably be 4chan. I’ve never been brave enough to visit 4chan myself, it is a scary place. A scary place with a large membership. Time found this out when they allowed the anonymous public to vote for Person of the Year. They could have settled with just picking someone outlandish, but what the 4channers did was way more impressive. You can read all about it in this post on musicmachinery.com.
There are some people who want to vote for public officials via the internet. I know that such a vote would be a different circumstance from the time.com poll. Which is part of the problem. How would the election officials ensure one vote per voter? How are you supposed to remember a password that you’d use (at most) twice per year? How do you provide an audit trail while preserving the anonymity of the voter? At some point, we’re going to reach that point. There are just issues to solve first.