I have seen it is possible to fly demilitarized Russian fighter jets in the US. Why is it impossible to fly American demilitarized fighter jets?
That's because US military is particularly concerned about chopping up its assets before civilians can lay their hands on them. The procedures are covered in US DoD Manual 4160.28 Defense Demilitarization: Procedural Guidance.
The procedures for 'demilitarizing' military aircraft are particularly brutal:
(a) Aircraft (Figure 29 and Figure 30) that are specifically designed for military purposes shall be demilitarized as follows: at a minimum, cut or break completely through at least one lobe of the fuselage trifurcated horizontal and vertical stabilizer spar attachment fittings, on both the right and the left hand sides of the stabilizer carry-through spar assemblies. This demarcation of the prescribed DEMIL procedures is to ensure the aircraft is rendered unfit for flight.
Demilitarization Procedure; image from Popular Mechanics
(b) Helicopters (Figure 31) specifically designed for military purposes shall be demilitarized by crushing, shredding, or smelting the entire airframe and fuselage, ensuring that the transmission mounts and supporting structural beams, engine deck in area of mounts, wing attaching mounts and support beam structure, and fuselage to tail boom attaching mounts and tail rotor gear ox mounts have been destroyed.
So basically, it boils down to the fact that the US military makes sure that the airframes won't fly again. Of course, there are ways around this- you can assemble the aircraft from parts or some aircraft will simply escape the procedure and is avialble:
In a letter to the chair of the House Armed Services Committee, AOPA President Phil Boyer ... stressed that certain aircraft (possibly aircraft not demilitarized) had been carefully maintained over the years and were now serving useful purposes.
but these are quite rare.
As the other have alluded, it is not impossible to fly demilitarized American military aircraft, it's just exceedingly difficult. Many are just not available due to the government holding the aircraft in reserve, and older ones are often limited by the availability of parts.
The FAA provides guidance for obtaining airworthiness approval for former military aircraft in AC 21-54 which is the first step in being able to fly such an aircraft.
Also as pointed out, the FAA doesn't have type ratings available for the majority of these aircraft so that poses a problem in being able to fly it once it's airworthy. The FAA addresses this using a Letter of Authorization or LOA. the process to obtaining this is defined in the following FAA documentation.
There are plenty of ex-military planes from many nations in private hands.
I know of an F4 being restored to flying condition by a private individual. He claims his will be the second in private hands.
A friend of mine owns an early MiG jet as well as a former Soviet trainer.
There have been several T-38s for sale from various online sources.
There are privately held T-33s out there.
At least one F-86. A few MiG-21s. At least one F-100. At least one F-104. At least one MiG-29. At least one Harrier. At least one F-8. A couple A-4s.
There is at least one Cobra flying around privately as well. Saw it a few weeks ago.
The list goes on...
There was a proposal sometime back to convert obsolete A-10s to fire fighting tankers. The outfit was, shall we say, "well connected" but it ended up not going anywhere. It would have made a GREAT, albeit pricey, tanker platform if I do say so myself.
The Wikipedia article on the Lockheed F104 Starfighter mentions a privately owned example in the US.