Most electronic devices use constant voltage source as power supplies. Why do LEDs require constant current source?
Oh, you can drive an LED with a contant voltage. It's only that this voltage has to be in a very narrow band, depends on chip temperature and is not easy to regulate.
Look at the I/U chart of a small power white LED. See how the current varies between 1µA and 10mA (nominal current) in the small band between 2.25V and 2.5V? And how much it depends on temperature? And how the power and the excess heat also vary 1:10.000 ?
So, it's much simpler to look at the current directly. That's why the current is measured and regulated (or simply limited with a resistor.)
Physics determines the I-V characteristics of a diode. It's not like the LED designers/manufacturers have a choice in the matter.
An LED follows the Shockley equation (with added series resistance) like any other diode, albeit with a much lower Is than a silicon diode (resulting in a higher voltage for a given forward current).
A relatively small number of LEDs have been made with an added series device inside the package that allows them to be connected directly to a range of voltages, however they have never been very popular. It adds cost (probably the biggest disadvantage) and limits the LED to a single approximate brightness.
Essentially, the current is proportional to the brilliance whereas the voltage drop is a varying characteristic from device to device.
This is not the only device that requires/benefits from constant current control. But many/most active devices use transistors as the control device and circuits can be most usefully made with these current-varying transistors operating from a constant voltage supply. That's why constant-voltage demand-led current systems are so prevalent.