Why did the first Space shuttle enterprise have a enclosed exterior compartment where the rocket engines are?

Answer 1

This was known as the tailcone, and was an aerodynamic shroud for early test flights.

Enterprise was never a spaceworthy vehicle. It was designed to test the characteristics of the shuttle in the atmosphere following re-entry. Its initial tests were to look at the shape of the orbiter itself and its aerodynamic behaviour, and the engines were omitted to avoid complicating the tests. In the final two test flights simulated engines were put in place, the earlier flights having verified that there was no inherent aerodynamic instability from the shape of the shuttle itself.

Answer 2

JasonT is right