Today, electronic systems use constant voltage power source. Current consumption varies as power consumption varies. Why can't electronic systems be designed the other way round? Using constant current power source and varying the voltage as power consumption varies. What are the pros and cons of each approach? Why has current electronic systems evolve to use constant voltage power source?
Most power sources are constant voltage, and not constant current. If you take the two main sources of electrical energy, which are batteries and rotating generators(regardless of size), the one thing in common is that their voltage is fixed theoretically to a certain value and can be controlled. For example, a standard AA dry-cell battery has a voltage of 1.5 V, which it will always produce more or less (disregarding real-life errors). The internal chemistry of most batteries relates the internal chemical reactions to the output voltage of the battery. Similarly the generator, for a given magnetic field strength (called excitation), and a given speed, will produce a fixed voltage at its terminals(again, only approximately due to real-life).
In almost any electricity-using device, in almost most cases, a voltage is the cause, and the current is the effect. Only when you apply a voltage to a device, may current start flowing through it (superconductors not-withstanding). Even constant current devices monitor the current and regulate the voltage as per the load. You never hear of a 3 V flashlight battery monitoring the voltage at its terminals. This is due to basic physics, in which change in movement of electrons (i.e. current) is possible when electric field (i.e. voltage) is applied.
While there's no reason why you couldn't design electronics with constant current sources, there's a few good reasons why we don't. Batteries and mains power are supplied more as constant voltage sources than constant current sources so it's simply more convenient to use what we have. The other reason is that a constant current source is always burning power. To shut a device off, you would have to short-circuit the power-supply. Since most wires have resistance, you'd constantly be wasting power.
The constant voltage method provides the key to load-line design of amplifiers. Given the vast need for amplifiers, the ability to provide stable gain for boosting long-distance phoneline signal strengths, the need for low distortion operation of vacuum tubes in those phoneline circuits, we may feel hobbled by the successes of BellLabs. But then Bell provided the transistor. Here is a load-line.
Such systems are in use in LED lighting applications (LEDs behave exactly like your question suggests natively), and they also were very relevant in the last decades of widespread vacuum tube technology (50s,60s,70s) - 300mA and 150mA series heater designs (which, however, were usually manually adjusted with resistors instead of using a proper regulated current source) were very common in consumer equipment.
You are thinking about voltage and current as a more closely related thing than they actually are. Voltage is a "static" potential. Current on the other hand is the motion of charges due to the effect of a voltage. For a given load in a circuit they are related by ohm's law, but they are physically different entities.
A voltage can, and does, exist when there is no current present. However, other than at absolute zero, a current can not exist without a voltage.
That is, Voltage is the primary object, current is the secondary.
Some circuits ARE designed to be powered by a constant current source. Many transducers like motors and LEDs are driven that way because their energy conversion characteristics are dependent on current, not voltage. However, it is important to note that constant current sources are controlled by voltage effects.
However, most electrical parts have characteristics that are fundamentally affected by voltage, especially capacitors and the conductance of semi-conductors. As such it is a lot easier to implement complex circuitry using a constant voltage supply and allow the current consumed to vary as it may.
Were you to try and build the same sort of circuitry using a constant current power supply, when one part of the system demands more power, it's resistance drops, the voltage would need to fall system wide to maintain the same current output from the regulator. This would change the references for all the remaining circuitry and affect how the capacitances and semiconductors behave in them. If it falls too low some semi-conductors would stop working.
As such, your constant current source would need to be designed to be at least your maximum system load.
Now you have the opposite problem. If that load dropped to a much lower level because you turned something off, your circuit resistance would be much larger, and so your system voltage would have to grow to a much larger value. All your components would need to be designed to deal with those larger voltages. If it goes too high your semiconductors again may suddenly stop working.
Further, if you had an ideal constant current source, as your load approaches a very high resistance, the voltage starts to approach infinitely. At which point physics takes over, insulators fail, and everything would self destruct. In reality what would actually happen would be the regulator would no longer be able to supply the current because it does not have the voltage to draw from to drive the output that high.
The alternative to that would be to not turn things on and off but to redirect it elsewhere instead, which, as well as being a waste of energy, is also extremely difficult to do while maintaining a constant total current. Further every little logic gate and amplifier would need do to the same thing.
In a constant voltage system each circuit contained within it is, to the most part, immune to what other parts of the system are doing. If a circuit on the right side of the board suddenly draws more current, and the regulator can supply it, and the board is designed correctly, the circuit on the left side is blissfully unaware of it. (Well almost.)
The bottom line is, in almost all cases, voltage, being the prime mover, is the thing that makes most sense to regulate and is a lot easier to control.
Lets imagine two outlets on a common house plug, fed by a constant current source somewhere further up the line, lets assume it's a 10A constant current source. When not in use the outlet needs to be shorted such that the voltage is zero (lets assume ideal wires for now). When you plug something into one outlet, you now need to un-short it, and allow the voltage to rise - lets assume you have a 10V 10A -> 100W lightbulb plugged in, and the act of plugging it in moves the short-circuit system out of the outlet. Now what happens when you plug in a second 100W lightbulb (10A, 10V) - the lightbulb now needs to function at 5A 20V - it needs to lower it's own resistance - and so does the other one - but how much? well it depends on the other device that was plugged in - the two basically need to stabilize, which while possible, is a very complicated system for a device as basic as a lightbulb, not to mention the special socket that would be needed to short closed when all devices are removed. This sort of current-voltage balancing system would need to be done for every splitter, leading to some complicated systems that need to balance themselves.
Now, I was ignoring wire resistance, but lets bring it back - you will always be running your wires at their maximum (since wires are rated by amps running through them for the most part) - this is not ideal, as using something at 24x7 to it's maximum is generally not good for it's lifespan, so you will need to increase the size of all the wiring to support this. Beyond the wiring you will also need to be able to quickly and reliably switch at 10A currents - 10A is a fair amount of current, which ends up causing sparks / arcing, thus wearing out switches fairly quickly, which brings me to another point.
Right now most mains power is AC, in that it has a zero-crossing - but you won't be able to instantly change 10A of current into -10A due to wire (and device) inductance. Large appliances can adjust their "power on" time to the frequency of the mains power, such that their switches (or relays / mosfets / whatever) turn on when the voltage is at or near 0, in order to prevent surges into say a capacitor bank that then feeds the system during the next 0V cycle. While I won't say that this is impossible, it would be quite difficult at best.