If LEDs aren't discharge lamps so why they can't be dimmed by using a regular dimmers. 12V halogen lamps still can be dimmed by regular dimmers despite they are operated by tranformers. The same case should be also in LEDs which are operated by similar tranformers (Called "Drivers" in Israel).

They can be dimmed (AND pick up increased efficiency when dimmed) but the drivers aren't generally designed for it. You could make your own.

Are you sure that the LEDs can be dimmed by using a regular incandescent and halogen lamp dimmer but their drivers aren't designed for that? Most LEDs retrofit lamps can't be dimmed by GLS dimmers and Electronic HF drivers that allow dimming of LEDs uses the motheds of dimming fluorescent and HID lamps (Ie.. PWM, 1V-10V and digital communication with the drivers like DALI and DMX-512 which are designed for dimming dischrge lamps). Even dimming LED flashlights (Like my LRI photon freedom micro) use PWM to dim their LEDs instead of regular dimming.

LED themselves could be dimmed, same as discharge lamps. The problem with incandescent dimmer switches is, then LED's, same as discharges, need a ballast to operate on mains voltage. So if you want dimming feature, you need to use dimmable ballast. And dimmable ballast does not mean using fixed output ballast with the incandescent dimmer, such combination would end up with a lot of smoke, but it is about incompatibility between the dimmer and ballast.

In special "dimmable" CFL's is used ballast specially designed to work with phase-cut dimmers, it has circuitry to decently extract power and brightness control signal from the waveform produced by the dimmer, so it work with phase-cut dimmers (most incandescent dimmers).
So in order to dim LED's by regular dimmers, you have to use those (with their ballast) specifically designed for operation with regular dimmer.
Note, then the same ballast would not work with "low disturbance" autotransformer dimmer.

But as the technology progress, it start to be more apparent, then the concept of phase-cut dimmer has very severe drawbacks (high disturbance with capacitance on the load, complex and expensive lamp ballast front-end,...), then for new installation is way more practical to use separate wiring for power (with direct mains voltage, maximum with power switch) and separate control circuity (1..10V, PWM, DALI,...), so all new dimmable ballasts are designed for one (or more) of these systems

So i understanding that LEDs also needs a current limiter device (exactly like discharge lamps) to operate them. Ballast (Driver, electronic usually) to operate them from the mains voltage and a resistor to operate them directly from a battery. This is because LEDs like dischages are not limiting their curret and with a simple step-down transformer or a connection without a resistor to a battery their current, like discharges, will continuesly increase until the LEDs will be distroyed or in case of main voltage the main switch will be tripped because the LED like the discharge is also an electric short.