We should definitely build ships capable of getting back and forth from planets in our solar system, but there's no reason to make them the shape of Enterprise just because.
I disagree that space exploration is a huge monetary drain with no practical return. You could apply the same argument to the moon landing, and it not only produced lots of modern technologies, it got us all curious about exploring space and expanding our horizons beyond our own planet. A ship that can go back and forth from Mars is just the next step in that continuum.
Now, if we want to go to other solar systems we have to deal with the small issue of time dilation first.