The light tank as a cheaper and more numerous version of a medium tank was obsolete by the end of WWII. The Germans were one of the first to stop building classical light tanks, the USSR followed soon after in the fall of 1943. The USA was the only major tank building nation to continue light tank development. The result of this development was the Light Tank M24, the best light tank of WWII. Its success is underlined by its longevity: some nations kept theirs in service into the 21st century!
Less armour, more gun
Military vehicles in multiple nations were developed along the same path. This applies to light tanks as well. It's hard to say that the USA was special in this regard. A successful design was used as a starting point and development went from there. The Light Tank T2E1 concept was refined over the course of eight years, leading to the development of the Light Tank M5A1. This tank was produced up until the summer of 1944 and became the most numerous American light tank variant. This was a true American light tank: fast, not that well armoured, and with a low caliber gun, albeit the most powerful in its class. The Americans didn't escape the temptation of making a light tank with the armour and armament of a medium one. That is how the Light Tank T7 was created and later evolved into the Medium Tank T7. The Americans were the only ones who took this idea to its logical conclusion (the T-50 doesn't count, as it still had the armament of a light tank).
The story of the Medium Tank M7 was a sad one, but it warned the American military away from such experiments in the future. However, there was another light tank that never moved past the design stage. This was the Light Tank T21 (a Medium Tank T20 lightened to 21,319 kg). This idea was born in February of 1943, but did not live for long. The Ordnance Committee saw that the Light Tank T21 was following down the road of the Medium Tank M7, and so the program was closed.