The Italians did just that actually, while not directly adding a turret mount to an L3 chassis, a new tank based of the L3 Tankette design with a rotating turret was made instead, called the L6/40, with a 20mm Breda 35 Autocannon mounted as the main armament, a good upgrade from the 6.5 mm machine gun the L3/33 was armed with.

This design was to fill the orders for light, turreted reconnaissance vehicles for the Italian Army, but only a few hundred vehicles were completed throughout the course of WW2, with most of them serving with the Italian Expeditionary Force in the Eastern Front against the Soviets.

As for why so few L6 tanks were produced, it was already outclassed before the war started, with the 20mm Autocannon having no hope of penetrating Allied vehicles such as the British Crusader and Churchill tanks, or the Soviets T-34's and KV-1's, so production was geared more towards the medium series tanks, the M13/40, M14/41, and M15/42. By as early as 1941, there was almost no point in making the L6 tanks as they were hopelessly outgunned by their British and Soviet counterparts.

Needless to say their medium tanks became outdated too upon the introduction of the American M4 tanks to the battlefields in North Africa, and Italian armor was unable to deploy effective counters to these new tanks in large enough numbers before their surrender in 1943.