In order to understand why the USSR had so many light tanks by WWII we need to go back to the early days of the Soviet armoured forces. The RSFSR realized the value of armoured fighting vehicles during the Russian Civil War, but Russian heavy industry was in dire straits to begin with, and the war didn't help. As a result, only a handful of Renault FT clones were built that never got to fight in the war anyway. The MS-1 tank built some time afterwards was no longer a clone of a foreign vehicle and resulted in valuable experience for the nascent Soviet tank forces, even though it in itself was not entirely satisfactory. Production and use of this tank allowed the Red Army to develop a list of requirements for tanks they would use in the future. These tanks were:

• Reconnaissance tank armed with one machine gun. This tank was an amphibious tank and therefore had to be relatively light.

• Combined arms tank with either a 45 mm gun or a 76 mm low velocity gun and one machine gun.

• Operational tank with either a 45 mm gun or a 76 mm low velocity gun and three machine guns.

• Tactical reserve tank with a 76 mm gun and three machine guns.

• Powerful special purpose tank with either one 76 mm gun and 2 45 mm guns or one 152 mm gun and one 45 mm gun and 5-6 machine guns.

The ideal operation would look like this: the enemy's main line of defense would be broken with a powerful combined arms assault of infantry, artillery, air, and armour. The reserve tanks would form the tip of the spearhead and smash whatever anti-tank defenses the enemy still had up after an artillery strike. The infantry and tanks of the second wave would mostly have to deal with mopping up small pockets of poorly organized resistance, so bulletproof armour was enough for them. The operational tanks introduced into the breach in order to execute long-range raids against the enemy's rear echelons would never come up against a well established anti-tank defense and would mostly engage an unprepared enemy. For these tanks, speed was paramount, their armour only needed to resist armour piercing bullets. Only the heavier reserve tanks needed armour powerful enough to resist artillery, and there wasn't much in the realm of anti-tank guns available yet. The most powerful weapon known in the USSR was the British 47 mm gun, which had a relatively low muzzle velocity and penetrated up to 30 mm of armour.

If you're familiar with Soviet tank design, you can probably figure out where the tanks slot in. The T-37A and later the T-38 tanks filled the recon role, the T-26 tank was the combined arms tank (a 76 mm gun version was tested but never panned out), the BT series of tanks was used in the operational role (BT-7 tanks were built with 76 mm guns, but not very many), the T-28 was the tactical reserve tank, and the T-35 was the special purpose tank. The amount of tanks built reflected how specialized their role would be: the BT and T-26 were built by the thousands, while only some 500 T-28s were built and just 59 T-35s.

This system of armament was upset by a revelation during the Spanish Civil War. Even though enemy tanks were armed with just machine guns, high caliber machine guns in the .50 cal or 12.7 mm class, autocannons in the 20 mm class, and even high velocity anti-tank guns in the 37 mm class became common. Work began on heavier armoured vehicles that eventually led to the KV-1 and the T-34 that you mentioned. However, designing a revolutionary new tank (or tanks) takes a very long time, so the T-38, T-26, and BT remained in production for the time being even though the Red Army realized that these tanks were not adequately protected against all threats encountered on the battlefield by 1938.

A whole slew of armoured vehicles were accepted into service in 1939-40. The KV-1 would replace the T-28 and T-35, the T-34 would replace the BT, the T-50 would replace the T-26, the T-40 would replace the T-38. However, replacing the existing light tank fleet was easier said than done. These tanks were heavier and more complex than the ones they replaced. For instance, just 892 T-34 tanks were in service by June 1st, 1941, a drop in the bucket compared to the 7500 BT tanks of various marks still in service. Production of the T-50 hadn't even started yet. 434 KV tanks were in service already, but there were still 481 T-28s left to replace. It would be years before the Red Army would have fully transitioned to a new generation of tanks.

Now, the question is, was the USSR unique in its number of light tanks in service? The answer is no. Germany is often lauded for its powerfullly armoured vehicles, but their tanks weren't much better. The backbone of the German tank forces was composed of light Pz.Kpfw.I and Pz.Kpfw.II tanks with bulletproof armour. Czechoslovakian tanks pressed into German service had up to 25 mm of armour, even German medium tanks had just 30 mm of armour in their strongest sections, and many had even less. Tanks with up to 50 mm of armour were just becoming available in 1941. Italy was in a similar boat, with their "medium" M 11-39 tanks being comparable to light tanks of other nations. The United States also made their bet on fast and thinly armoured light tanks, with only a few dozen Medium Tanks M2 available at the start of the war, and even these had up to 25 mm of armour. Even the UK had the backbone of its armoured forces composed of Light Tanks Mk.VI and Cruiser Mk.III and IV tanks that would be considered light tanks by most foreign standards. France is in a bit of a weird place, since their understanding of what a light tank is was different than that of other nations, but even they mostly produced 10-ton class Renault and Hotchkiss tanks with heavier/better armed/better armoured SOMUA S 35 and B1 tanks remaining specialist vehicles produced in relatively small numbers.

To summarize: the USSR had a large fleet of light tanks by the start of WWII because the demand for heavier tanks with better armour only rose in the late 1930s. Most WWII belligerents were in the same boat and shifted from production of lightly armoured tanks to heavier armoured medium tanks only towards the end of the 1930s and the start of the war.

Sources:

http://www.tankarchives.ca/2014/08/state-of-affairs-1932.html

http://www.tankarchives.ca/2014/09/tank-quotas-in-1931.html

http://www.tankarchives.ca/2014/12/soviet-tank-production-1932.html

http://www.tankarchives.ca/2016/09/second-five-year-plan.html

https://www.tankarchives.ca/2020/08/new-tanks.html

http://www.tankarchives.ca/2017/12/tougher-armour.html

https://www.tankarchives.ca/2019/03/future-of-soviet-tanks.html

http://www.tankarchives.ca/2015/07/common-questions-red-army-afvs-in.html