Part of the problem is light tank battalions requiring 60 tanks. Not sure there is any justification for this other than it being a quick balance kludge that just stuck around.
TLDR it made sense before Tank Designer.
I don't really agree with it being an exploit. It's definitely an optimization trick, but I wouldn't go so far as to call it an exploit. To my knowledge, everyone in multiplayer does it if you're in a high skill game and it's widely accepted. If it was considered an exploit it would probably be banned by house rules, but it isn't. It's just using the game systems as designed in a way that benefits the player.
I think we should differentiate between exploit (using game mechanics directly against the way they were designed to be used, with high disregard to realism, believability or historicity, irrespectively of what one think about these concepts) and cheating (breaking rules agreed upon by all participating players). I stand in position that training tank crews without tanks fulfill definition of exploit, and its common usage in highly competitive multiplayer environment doesn't make it less exploit, it just make it aligned with rules agreed upon by all participating players.
generally it's bad game design to include choices (making lights as opposed to not making them, especially after ~1937) which are unconditionally worse to make.
I think this is simplicitic view. In any game complex enough, there will be options that are strictly worse than any other. You can use 50-width heavy tanks only divisions to hold the line, but would that be optimal? You can never build any military factory, but would that be optimal? Therefore, you can build weapon system that was slowly becoming obsolete as per 1939 well into 1944, but do it really has to be viable option?
That being said, I agree that light vs medium costs as-presented by
@blahmaster6k are off. My wild guess is that both of them are ahistorically strong, and that maybe Reliability is not important enough - with Reliability at 50% (against 83%), actual cost of maintaining force of mediums equal in numbers to force of lights should be 66% higher than cost as-presented, for about 2 times cost of light, as you postulate. So I guess you both convinced me.
I'm not much of a history guy but it also is my understanding that often throughout the war mediums saw success against strictly stronger heavies simply by there being more of the former, in part a product of their lower cost. why wouldn't that apply to lights against mediums too?
Difference is, medium tank is standard tank, while heavy tank is specialized weapon system expected to be used in schwerpunkt. Low availability of heavy tanks, while not optimal, is acceptable. But medium tank that is produced in small numbers or is not reliable is as good as medium tank that can be penetrated by rifle fire, or cannot penetrate 20mm of armor at good range, or move 4km/h.
There are two direct results. First, if you take all german heavy tank battalions, from any point in time, I doubt you could fill one 80-width province with them. But that's ok, you don't need them to fill frontage, you need just enough, with other arms, to break enemy line at one province. But it also means there is nothing particularly strange with achieving numerical superiority over them.
Second, while much emphasis is put to tank-on-tank actions, that is not what mediums were historically for. Medium tanks are not anti-tank weapons, through they are quite good at it. They are universal war machines, expected to kill tanks, infantry, light armored vehicles and fortifications, while withstanding artillery and airstrikes. Its not enough to saw success against them, to be viable alternative, your light tanks have to be - after taking their bigger number into account - better at fighting infantry, withstanding anti-tank fire, withstanding artillery, and only then at killing mediums, and they have to do that more or less on the whole frontline at once.
TLDR there is not direct analogy.
