The only time you really need medium or heavy tanks is to fight other medium or heavy tanks. Light tanks do very well against soft targets like infantry so if the bulk of your opposition is soft targets then heavy tanks won't help anyway. Tanks have amazing breakthrough stats so they're excellent on attack and shit on defense. I usually use an army of 8-12 tank divisions to take greound and infantry divisions to hold it afterwards.
Are tanks actually useful at all? Like... Infantry has the best stats, by far. I mean... building a large army of mechanized or motorized infantry with armor support is almost hamstringing yourself in this game. I think tanks need a major buff.
Also... I can't stop playing the Dutch, they're so fun! Democratic Dutch, Fascist Dutch, and soon... Communist Dutch. They're great!
WW2 strategy lesson (not yet tested in the game because I'm doing the 1936 start), but its difficult to decisively destroy enemy units unless you surround them. This is the best way to achieve fast results in terms of breaking enemy resistance. Surrounded units will not only be vulnerable to attack from multiple directions, but they'll run out of supply (abstracted in HoI to originate from the capital, or at least it was in 3). The threat of encirclement, even without the execution, allows you to force an entrenched line of enemies into retreat. Once you've broken their line at two points, you threaten to form a circle around a stationary defensive line, basically dooming them unless they can break open the circle and push out. So even with fortifications and entrenchment you can force them to retreat.
The purpose of tanks is to apply a lot of pressure on one point and break through, to facilitate encirclement. However you put yourself in a tight place once you do this, as that thin line extending into enemy territory can be "pinched" at the breakthrough point (turning the tables and encircling you). You need fast units to take advantage of a breach in enemy lines before they form new lines, but tanks are generally too expensive to be wasted occupying a bunch of loosely or not defended enemy provinces. That's where motorized infantry or other "exploitation" units come in. They don't fight much better than infantry, but they can rush through a hole in the enemy line and carry out an encirclement or claim territory before the enemy's leg infantry can respond effectively.
Most of you that ninja'ed me knew all that, but I'm sure plenty reading this thread didn't so I'll leave it.
The other thing that tanks are useful for is increasing a division's "hardness" rating. I don't know exact formulas but a basic way to think about it is representing the proportion of soft attacks vs hard attacks an enemy will be making. Towed AT adds hard attacks but it does NOT add any significant amount of hardness. You need tanks (or tank destroyers) because they're the only way to increase hardness rating. An entirely soft army is arty fodder.