I feel that the idea of feedback is not far from the truth, but a better description would be "equilibrium". All electrical systems will (almost instantly) adopt a state which conforms with the so-called "lumped element model", consisting of Kirchhoff's current and voltage laws (KVL and KCL), and the equations we have applying to elements like voltage sources, resistors (Ohm's law) and diodes (the Shockley equation).
However, the lumped element model does not explain why this equilibrium is obtained, and why it seems to maintain itself in spite of noise and other environmental perturbations that might destabilise it.
First, let's examine how the lumped element model is used to describe the system algebraically, and then we'll look at your idea of "feedback", and my suggestion of "equilibrium". Here's the arrangement:
simulate this circuit – Schematic created using CircuitLab
The supply is \$V_S\$, and according to KVL, the sum of voltages across the resistor and diode, \$V_R\$ and \$V_D\$, must equal \$V_S\$:
$$ V_R + V_D = V_S $$
There's nothing mysterious or arcane about this. Voltage is just a measure of potential energy (of charges), just as your altitude (say, above sea level) is a measure of how much gravitational potential energy you have. If you start at point X somewhere, and take a walk around a big loop back to X, going up and down hills, steps, or whatever causes you to gain or lose altitude, then when you arrive back at X you must have the same altitude you started with, and the same potential energy. That's the principle being described by KVL, but for electric charges.
KCL is even simpler to apply here. Given that there's no path for current to enter or leave the loop, current \$I\$ must be the same at all points around the loop. Again, this is a principle you see at work in many places, like water in a closed loop; if there's nowhere for water to leave or enter, then the number of litres flowing past each point, each second, must be the same everywhere. Otherwise you're getting new water for free, or losing it somehow.
KVL and KCL are always obeyed, just as physical laws that you are more familiar with (like altitude or water flow) are always obeyed. The only real difference is that instead of molecules with mass moving in a gravitational field, KVL and KCL deal in particles with electric charge moving in electric fields.
The last piece of the lumped element model is the relationship between current and voltage for each individual component. The equations we obtained from applying KCL and KVL are not related to each other; they don't share any variables, and can't be "solved" without more information. It's up to the various components in the system to define the relationship between currents referred to in the KCL equations, with voltages mentioned in the KVL equations.
For the voltage source (a battery in my schematic above), there is no relationship to speak of between current and voltage. Any amount of current can flow through it, and that won't change the potential difference across it at all. However that does mean we have a well defined and fixed value for \$V_S\$:
$$ V_S = 12V $$
For the resistor R1, there is a very simple relationship, Ohm's law, allowing us to define voltage \$V_R\$ unambiguously, as a function of current \$I\$ through it:
$$ V_R = I \times R_1 $$
Finally you have diode D1 to deal with, which also has a very well defined \$I\$-\$V\$ relationship, the Shockley diode equation, which will be some variation of:
$$ I = I_S\left(e^{\frac{V_D}{\eta V_T}}-1 \right) $$
Sometimes you see \$V_D\$ as the subject, which may or may not be more useful here:
$$ V_D = \eta V_T \cdot ln\left( 1 + \frac{I}{I_S} \right) $$
So these are the equations that describe the system:
$$
\begin{aligned}
V_S &= 12V \\ \\
V_S &= V_R + V_D \\ \\
V_R &= I \times R_1 \\ \\
V_D &= \eta V_T \cdot ln\left( 1 + \frac{I}{I_S} \right) \\ \\
\end{aligned}
$$
These are all the conditions that must prevail for this system to obey the laws of physics, as we understand them: the lumped element model. The system must settle into a state that satisfies all these conditions simultaneously, which gives rise to the term "simultaneous equations". If you solve them you will find that \$V_D\approx 0.7V\$ over a large range of values for \$R_1\$ and \$V_S\$. That's just the maths talking, but it doesn't explain why.
I probably didn't need to say all that, because where I go from here is the real answer. Still, I'll leave it in for completeness.
Those equations describe the state of equilibrium that this circuit will attain, and maintain, but do not in themselves explain why. So, why is the system stable, obeying these laws?
The lumped element model does not deal with individual particles. It is describing the average behaviour of huge, huge numbers of electrical charges. The model doesn't describe the potential energy of any individual charge. It deals with the average energy level (voltage) of a large number of charges at some point in a circuit. The model describes the migration (current) of many charges, not any individual one.
You could treat particles individually, but you would have so many equations that no amount of computing power could solve for their positions and velocities. When you consider that each charge is a quantum particle, subject to quantum effects, there will be many of them that seem to move in the wrong direction, or to magically teleport, or do any number of weird things. There are waves of potential, regions of compression and rarefaction of charges that travel and reflect, refract and diffract, and interfere with each other, as all waves do. It's a mess.
And yet, on average, when observed all together, the combined behaviour of all those charges always averages out to conform to a set of much, much simpler concepts which we called the lumped element model. Potentials, the superposition of all those potential waves, is predictable, even though the individual charges and their waves of motion are unimaginably complex. Average charge motion, which we call current, is remarkably consistent, in spite of those charges zipping about in all directions seemingly at random.
There is a kind of self-regulation happening in all that pandemonium. If a single electron jumps out of place, the resulting change in electric field will cause other neighbouring charges to experience a change in force upon them, which cause others further out to react, and so on. This forms a wave of potential propagating outwards, and as I mentioned, that wave will reflect and refract and diffract, and importantly, to interfere with other waves, and even itself. An equilibrium is maintained because any single electron out of place will cause waves that will ultimately interfere with each other, and in superposition retain a stable, ordered, and predictable state. This is a kind of self-regulating, negative feedback inherent in all physical systems, keeping order at larger scales, where there is underlying chaos.
It's like the surface of a pond that is perturbed, causing waves to propagate outwards. There are reflections of those waves from the shore that return to restore the water's depth where the perturbation originated. There will be oscillations about some average depth, and eventually those oscillations will die away, but the average depth of the pond remains unchanged over time.
In this way perturbations to the system do not persist. An increase in resistor voltage \$V_R\$ does increase current \$I\$, which will in turn increase diode voltage \$V_D\$, but that increase of \$V_D\$ must in turn result in a decrease of \$V_R\$ to its original state. It might be tempting to say that that's because KVL would be violated, the system must return to a state compatible with KVL, but that's assuming the lumped element model can account for this; it can't because it's just a set of equations.
What's really happening is a propagation of waves carrying energy throughout the system, which, as a whole, will always act to restore an equilibrium. That equilibrium is, in physics terms, a state of lowest potential energy, to which all systems (physical, electrical or otherwise) tend over time, and it is this state that is described by the lumped element model. In this diode example, the state \$V_D\approx 0.7V\$ is the state of lowest potential energy for the system as a whole, and it would take energy from outside the system to change that.
The diode equation is just part of the lumped element model that describes and encapsulates this characteristic, but is not ultimately the a-priori reason why \$V_D\approx 0.7V\$. The real reason is that the system will "find", or "home in on" the state of lowest potential energy of the entire system, voltage source, resistor and all, which happens to be when \$V_D\approx 0.7V\$.
