You have two questions wrapped up in one. First, what would be the benefits / detriments of such a system? And second, why hasn't such a thing been implemented?
One large benefit could be increased participation and political efficiency. Right now you can vote every 2-4 years, write your congressman or local official, or start a protest or media campaign. These are high-cost actions with little perceived effectiveness on the part of most ordinary people, which explains why some people don't even bother to vote, much less participate in a petition, rally, or other political movement. But if expressing your political opinion was as easy as writing a restaurant review on Yelp, and as effective as Yelp in getting restaurants to respond, you can imagine how enthusiastically most people might participate. High participation would in turn provide government agents and politicians with a clearer indication of what voters want, and also increase their sense of accountability to those voters. General collective awareness about civic issues and trust in the system could increase as a result.
There's some potential detriments as well. First, nobody can be fully informed on all the issues, so how do you allow voters to make educated decisions or vote by proxy? Secondly, how can you protect the rights of minorities in a system where the will of the majority is easily determined? There are technical solutions to these problems, but the larger problem is that people would simply need to trust the system to work, which requires a working example.
Which leads to your second question. Why has there been no solution implemented as of yet?
Trust is one factor -- nobody has seen a working model for a national system (even though there are some municipal governments that are very progressive in this area), and so it's hard to garner widespread support for such a system.
By and far, however, the largest problem is that constitutionally the federal government has no support for such a system. Currently elected officials would have to muster the support for a bill or amendment and pass it into law. All currently elected officials won elections in the old fashioned way, and it's unlikely they would want to support a bill that would abolish the methods that allowed them to win. In other words, it's hard to change the status quo.
There's some ways to get around this. Some political entrepreneurs have tried to start "web 2.0" parties, where the party will vote according to deliberations on a website, but in general these have failed to win much popular support.
Personally, I think the most likely scenario is that either the Democrats or Republicans will find that adopting some software to allow more feedback from voters will improve their get-out-the-vote efforts on election day. This is a big area of investment for both parties, so it's not unrealistic to assume they might experiment with it in the next few election cycles. If one of the big parties were to adopt some software like this, the other would rapidly adopt it as well, and in that manner we might see a more online political process adopted rather quickly.