I appreciate that you can tag people on twitter, and reach a wider audience. But, social media is more than retweeting or favoriting. It is about replying, commenting and posting original content. Interacting, engaging, and building a following. And this will take more time and effort. Without creating interesting content, you are not going to gain a lot of followers.
People (as I hear it) seem to argue that followers are not that important. I disagree. Remember that there are algorithms in place that decide the impact of tweets. And when you retweet a tweet to a representative or organization, remember that they (like people here) are likely receiving more posts than they can read. So it becomes about priorities and impact.
Whose tweets are influencers and decision makers going to be reading, engaging with, or reacting to? It is likely to be high impact twitter accounts with many followers that can gain influence this way. So the way I see it, it would be better to have a team of dedicated people working on building one (or a few) high impact accounts, rather than trying to flood the twitterssphere with retweets from lots of low impact accounts.