Sorry, no mountain launchers on the near horizon.

Launching a mountain-sized object from Phobos, Mars, the moon, or Earth is beyond the capabilities of current technology and faces significant challenges. 

However, let's entertain the idea by analyzing the best-case and worst-case scenarios using a quantum simulation to assess feasibility, cost, appearance, and utility. 

Note that conducting a quantum simulation on a mountaineous object of this scale is currently impossible, but we can still explore the concept.

Scenario 1: Best Case Feasibility

Suppose we somehow succeeded in transporting a mountain-sized object to Phobos, hollowed it out to reduce mass, and fitted it with engines. 

We would still face daunting challenges:

1. Structural integrity: Mountains are not designed to fly. Significant reinforcement would be required to withstand the forces encountered during liftoff and flight.

2. Engine power: Mount Everest, for example, weighs approximately 3.5 quintillion kg (3.5 × 10^18 kg). With a gravity of 0.17g on Phobos, the object would still require colossal engines to generate enough thrust for escape velocity.

3. Trajectory and navigation: Precision control of such a large object would be incredibly difficult, especially during the ascent and insertion into a transfer orbit.

4. Cost: Given the energy, materials, and construction required, the expense would be astronomical.

Scenario 2: Worst Case Feasibility

Let's imagine that we attempted to launch a mountain from Phobos without addressing structural integrity, engine power, or trajectory.

1. Catastrophic failure: The mountain would likely collapse under its weight or disintegrate during liftoff, destroying the launch site and any nearby infrastructure.

2. Energy wasted: Billions of tons of debris would scatter across Phobos and Martian space, squandering precious resources and energy.

3. Environmental impact: Debris could impact Mars, moons, or other planets, polluting their surfaces and threatening future missions.

Appearance:

Visualizing a mountain-sized object in space is difficult, but we can try imagining Mount Everest hovering above the horizon of Phobos or Earth. 

The sheer scale would be breathtaking and terrifying, overwhelming the observer with awe and a newfound appreciation for the power of human ingenuity (or folly).

Utility:

Accessing valuable minerals inside a mountain-sized object is implausible, as mining techniques would need to be invented, and excavating would generate unmanageable volumes of rubble.

Technological Trajectory:

Mountain-scale launches are currently unimaginable. Realistically, we should expect smaller objects, like habitats or satellites, to be assembled in space using advanced materials and techniques before we even dream of moving mountains.

Overall, launching a mountain-sized object remains firmly in the realm of fantasy. Future technological advancements might permit the movement of smaller bodies, but mountains are simply too large and cumbersome for current or foreseeable technologies.