I’m not great at physics and have no knowledge of aeronautics, so this whole chain of reasoning might be wrong.
A plane stays in the air because air is moving over the wings, which generates lift. However, that air is moving because the engine is moving the plane forward. There is no other source of energy. Therefore, some of the engine’s energy is going into keeping the plane in the air, and some is going into accelerating it forwards, or keeping it at the same speed (fighting air resistance).
Therefore, if the plane points straight up, the engine should be able to support it hovering in the air. If it didn’t have enough power to fight gravity when pointing straight up, it wouldn’t have enough power to fight gravity when moving horizontally, either.
(Okay, some older engines only worked in certain orientations, but I don’t think that’s a problem for jet aircraft, or any aircraft built after WWII.)
So why can only certain planes fly vertically?
The plane staying in the air is due to lift. Lift is generated by the wings in a traditional aircraft. To generate that lift, air has to be moving over the wings at a particular rate.
Now consider this: in a car, train, etc., you can slowly accelerate up to a given speed. The smaller the engine, the longer it takes to accelerate up to speed X. The same is true in aircraft. Once the aircraft moves fast enough, the wings will produce enough lift to raise it.
For an aircraft engine to produce enough lift to lift the plane vertically is a different matter entirely. Because the wings are no longer producing lift, the propellers (assuming not a jet, but principles are the same) have to be the source of lift. Note that propellers themselves are little wings that produce lift from air flowing over them, but not the same amount of lift as larger wings.
tl;dr: an aircraft engine generally only needs to produce thrust to move the aircraft laterally quick enough so that the wings produce the lift. Without the wings, the math changes drastically.