The total work done by all forces acting on an object throughout the motion interval of interest is what the work-energy principle involves. It never says "no forces are doing work." And it doesn't talk about changes in potential energy. The changes in potential energy are involved in the work done by the conservative force attached to the particular potential energy. The bookkeeping of work, (force and direction and distance), can become tedious in some situations, but it works.
Let's say a person lifts a stationary box from a floor, carries it somewhere in the same room and sets it on a table. Let's also ignore air resistance, etc. The initial KE of the box in the table/room/floor reference frame is zero. The final KE of the box is zero. The total work done by all forces acting on the box is zero.
What forces did work on the box? AHA! The normal and frictional forces of the person's hands initially did positive work (force is up, motion is up), then more positive work as the person exerted a sideways force with sideways motion, and finally some negative work as the person exerted upward force to gently place the box on the table rather than dropping it. Gravity initially did negative work (gravity down, box moves up), and zero work as the box moved sideways (ignore the slight bouncing of the box while it's being carried) then positive work while the box moved down. All this work on the box adds to zero.
Meanwhile, the heart and brain and muscles were all doing work internal to the person, so they had to go get a soda pop and sit down and rest.
The state of constant motion along a straight path or being at rest defines a state of the system known as inertia. Force is some agency that disturbs the state of inertia. Force causes acceleration (precisely, a change in momentum). Newton's second law of motion states that
$$\vec{F}=\frac{d\vec{p}}{dt}$$
If the body is moving at a constant velocity, then there is no change in momentum and so
$$\frac{d\vec{p}}{dt}=0\implies\vec{F}=0$$
Hence constant motion means no external unbalanced force is acting on the body. Since there is no force, there is no work done (Since $W=\int\vec{F}\cdot d\vec{s}$).
Hence no work is necessary to be done on a body to maintain it at a constant speed, because no force is required for a body to move with constant velocity. There is displacement of course. The fact is that the displacement that happens here during a constant motion here is not the consequence of the force. The displacement term appearing in the equation of work:
$$\text{Work done}= \text{Force} \times \text{displacement along the direction of applied force}$$
is the displacement as a consequence of the applied force. The dot product between force and displacement (picks up the component of displacement in the direction of the force) vanishes if the force and displacement are independent of each other (or orthogonal to each other in some sense). Here the displacement happens not due to any force. So, the component of force that caused the displacement is zero. Hence there is no work done.
Then by the work energy theorem, there is no change in the kinetic energy of the body. Hence the conservation of energy. This makes sense. No work is done on the body as there is no force to do that. The body is under constant motion, which means momentum is conserved. That is, $p=\text{constant}\implies \Delta p=0$ and so $K.E=p^2/2m=\text{constant}\implies\Delta K.E=(\Delta p)^2/2m=0$.
Conclusions:
- An unbalanced force causes acceleration. It cannot make objects move at constant velocity. Constant velocity is achieved only in the absence of an external force.
- According to Newton's second law, a force is not necessary to keep an object in motion (there is motion, a constant one, possible even in the absence of a force). However the motion will be an unaccelerated one, and takes place along a straight line.
- So, in constant motion, the displacement is not due to some force. The force is absent and so the work done is zero.
- Since the object is moving at a constant velocity, its momentum is not changing, which means that the kinetic energy of the body is not changing. So work done is zero implies the change in kinetic energy is zero. Hence the work- energy theorem.
Best Answer
Both your equations are valid as long as you're dealing with conservative forces. They - pretty much by definition - express conservation of mechanical energy. There are other kinds of energy as well and in most realistic situations you need to take them into account as well. The total energy is always conserved and for conservative forces in classical mechanics, the only relevant types of energy (the ones that can change) are potential and kinetic energy. So the sum of those is conserved.
In the situation of the car the forces are not conservative and energy is lost through e.g. heat from friction in the engine. The potential energy that has been decreased is the chemical bond energy of the fuel. Fuel is being 'burned', i.e. bonds are being broken, and the energy that is released by this process is used to perform work. However, not all the energy is put to good use, there's losses from the system heating up (and that thermal energy is mostly released into the environment). There's also losses from friction of the wheels etc. but the total energy, minus the losses, is conserved.