Electronic – Why plug is polarized in the US? What are the benefits

As other posters have suggested, this can't be done via conductive measurement alone. However, non-contact AC testers will properly differentiate line from neutral without a reference ground via capacitive sensing. This type of hand-held tester often has a flat plastic blade at the tip. Inserting the blade in the line slot will cause the LED to glow; inserting in neutral or ground will not glow:

There are a number of kits for this type of circuit, as we as many sample schematics available in a few minutes of searching (Search string: non-contact ac voltage detector circuit). They're essentially just high gain amplifiers that drive an LED.

Using this type of sensor permanently mounted near the Neutral line can serve as an indicator that your plug has been inserted the wrong way, provided that you have a reliable way (i.e. not battery) of powering the circuit.

From wikipedia:

Supercapacitors are polarized and must operate with the correct polarity. Polarity is controlled by design with asymmetric electrodes, or, for symmetric electrodes, by a potential applied during manufacture.

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Polarity

Although the anode and cathode of symmetric supercapacitors consist of the same material, theoretically supercapacitors have no true polarity. Normally catastrophic failure does not occur, however reverse-charging a supercapacitor lowers its capacity. It is recommended practice to maintain the polarity resulting from a formation of the electrodes during production. Asymmetric supercapacitors are inherently polar.

Supercapacitors may not be operated with reverse polarity, precluding AC operation.

In other words, even for capacitors with symmetric electrode structures, there is a "charging" process during the manufacture that creates a asymmetric insulating layer inside the capacitor. You can reverse-charge a super capacitor, but doing so likely leads to a microscopic degradation of the specially prepared electrode surfaces (probably due to bizarre chemistry physics I don't understand), reducing the available capacitance.

I suspect this is similar to the process for manufacturing lead-acid batteries, where the plates are actually initially identical, and the initial charging process modifies the chemical properties of both plates. In their un-conditioned state, it's probably possible to electrochemically convert either electrode to the "positive" electrode, but once the electrode have been conditioned, trying to reverse their polarization would probably damage their chemical properties, and thus the capacitor.