After a dozen or so scenarios and staring the campaign, here are my revised thoughts:
It's often tough. The AI can exploit holes in your line and cut off your supply, and will ignore the likelihood of being cut off itself. So you need to pay attention to both your front line integrity and your supply sources. The AI isn't smart, but it is crafty. Often it withdraws front line units to protect objectives, when they would be better holding the front. It will extricate itself from potential pockets fairly well, though.
The AI sometimes moves units around the front unnecessarily. It will swap equal units for no apparent reason. It will also concentrate attacks on your weakest units (even if there are better targets on the line), so try to move strong units in and replace them before you end your turn.
You need to circulate units in battle. Attack, move the spent attacker out, and put a fresh unit in to continue the attack. This is a little different from how many boardgames work.
Rivers make attacks very, very costly. The AI is reluctant to attack across them or at high odds. When you have to breach a river defence, it can be tough, even impossible (for German allies in particular).
Specialty attachments and reinforcements are often critical to a scenario but the whole prestige point system sucks. It's ahistorical. It needs a rethink.
I really wish the game didn't just end when all the objectives were taken - I wish it gave you the opportunity to continue playing. I would also like to see different levels of victory.
I still want separate artillery units, not just have integral artillery support, especially for the Soviets. It feels unrealistic not to have Soviet artillery battering the front lines, especially when river or city defences are involved.
The Red Turn DLC has some different challenges, and the campaign seems easier. It also has a huge map for scenario creation.
The life so short, the craft so long to learn...
Chaucer, The Parliament of Fowles