I think the question is why should the broad general public be interested?
I think the reason for the desire for broad public interest is directly linked to the desire for continued and possible increased public funding.
I don't think this is sound reason. And it's based on a false premise.
I think it's similar to news coverage. Not enough people watched the news- so, the solution making news flashier and more entertaining. That's a bad idea. You might even get more people watching the news, but it's still a bad idea.
Instead the news should focus on providing better news. If you want news and entertainment do something like the Daily Show. That isn't news.
So, basically don't do what you aren't. Focus instead on your strength. NASA if interested in more public interest then should out source this task- such as get Discovery Channel access and it can promote it. Discovery has a vested interest in getting the public to watch it's shows. I.e it runs ads. And in general, puts effort into producing something people will watch. They are Pros. NASA is an amateur- and they should not even want to pros in this regard, it would be a distraction.
But instead of TV, NASA should be more interested in providing scientific data. Be an excellence resource for schools, collage level, and broad public. It should also focus on getting press release and info packets to various media outlets. It shouldn't focus on excitement, it should focus on being accurate [which it's very sloppy about at present].

The people who going to make space exploration "exciting" will be the private sector. They will make it exciting because it will be critical in their making money.