Well, as the petition for building a Death Star demonstrates, it's nice to wish for things. Wishing is easy and cheap. To actually make it happen....that requires realistic concerns be met.
As said in a certain well-known sci-fi novel (paraphrased): "When they voted for the impossible, the disasterously possible happened."
Even the more realistic designs in such series as Babylon 5 and Space:1999 are beyond our level of ability or will at the moment (we are going back to capsule spacecraft, for crying out loud!). The technical and engineering challenges inherent in a ship like a Constitution class ship is just too great for the current time.
Finally, until last month, there -was- a real-life U.S.S. Enterprise, and will be again:
And if you want to know just how hard it would be to build, maintain, operate, and supply what people are trying to use the petition system of the government to get, look into the complete logistical, engineering, operational, material, and personnel resources and proceedures involved in the real ships that do what the NCC-1701 did in fiction, and multiply them by 100.
Seriously, using the petition system as a toy kind of ticks me off, as I think it has a more important use than as gratification for people who know better.