There is some confusion about the principle behind tankettes. They were designed for a particular role, mainly that of "mobile pillbox" roving around the battlefield to counter infantry advances or even spearhead attacks, they were never meant to engage enemy AFVs, that was the job of artillery and AT weapons.
The concept was taken from WWI where machinegun positions were critical elements, it was therefore a logical conclusion that putting them under armour and on tracks would make them devastating weapons. They would operate in large numbers so that even if the enemy had AT weapons they would be able to overwhelm these before losses became significant.
The British had the Motor Machine Gun Service, which did very well in areas where the fighting hadn't bogged down in the trenches, the Tankette is therefore somewhat akin to the US Tank Destroyer Doctrine of using specialist AFV's for a specific purpose. The Tankette looked like the next logical step in the process, a modern, lightweight machinegun carrier, in British service it evolved into the Universal Carrier and acquired a more expanded role during the war. Oddly enough this is a good example of a vehicle which was mostly used for the role it was intended for (scouting, carrying a mobile MG behind armour etc) but is now mostly considered to be a mere troop carrier.
In those days the logic seemed sound, it had the speed of cavalry, the firepower of a machinegun and could even charge under fire, something the cavalry couldn't. If used as planned they did work reasonably well. But conditions in the field often dictated otherwise, like Tank Destroyers or even the Battlecruiser they were used for jobs they were not designed for and ended up fighting tanks.
We also have to acknowledge that for some War Departments and military commanders they quickly became "low budget tanks" as they could be built in vast numbers in regular automobile factories at low cost.
The original doctrine of these vehicles had become blurred and their failure rate so high that they were seen post war as a foolish mistake and somewhat arbitrarily lumped together with tanks, where there ought to have been a more honest distinction.