I’d go one step further, Switch. Infantry units most likely represent armies rather than divisions. If you look at the board to start the game, and assume that the pieces are meant to be commensurate with Germany’s deepest advance into Russia, then each one should represent 200-300 thousand soldiers. The starting units in the Ukraine, for example, represent Army Group South, which certainly had more than 3 Infantry Divisions.
What I’m saying does break down when you look at the Japanese islands (and Allied garrisons like Midway). The garrisons on most of them numbered in the tens of thousands, rather than the hundreds of thousands. However, the game has no way to reconcile these amounts, so we’re stuck with a 3 IPC Infantry unit to represent them all.
The other thing I’d add is that the logistical support of a unit is included in the price. Feeding an army of 200,000 men, providing operational intelligence, and keeping them resupplied with ammunition, clothing, replacements, etc. would all go into the 3 IPC cost.
I know I’m off topic, but I do think it’s fun to keep the scope of the game in mind.