The main problem is one of logic. The UK or America is usually always in a position to take Normandy and Southern France. Being on the coast and farther away from Germany and Italy’s major factories, they are almost impossible to fortify to prevent America from taking it if they want it. Fortifying Normandy and S.France means no offensive (or a weak one) against Russia.
As the Allies, if you are in a position to take France and hold it, it means your assault force is enough to hold off West Germany and Italy, which means you should probably just take West Germany or Italy. Otherwise you’re liberating Paris and turning around and handing a fistful of IPC back over to the Axis.
As America, Normandy’s factory is supremely important because it allows you to produce naval units in Sea Zone 110. This allows you to directly protect the UK (if they are in a weak defensive state) or produce capital ships for bombardment against Germany if you need them. You can effectively take Germany completely out of the water. I have had my navy ready to take Italy in the Med and successfully stopped a German re-invasion of the UK by performing Operation Instant Navy in SZ110, allowing me to not have to split my naval forces to defend the UK.
As far as IPC gain is concerned, that’s a no-brainer. With the rules in regards to occupying friendly territories and gaining their IPC, you really only stand to lose IPC as the Allies. As I posited in the FAQ thread, I think you could execute an Axis strategy that involved taking France and not capturing Normandy and Southern France. In the long run, you lose out on 5 IPC a turn for the brief time before an Allied power almost inevitably invades those two countries, but you save the IPC from not suffering casualties taking those two countries.
And if you’re worried about those forces coming back to attack you, the forces you didn’t use attacking them are the same ones you’ll use defending. You can always throw 1-2 infantry at those two and strafe them with aircraft or have Italy help. Altogether those two countries only account for 2 infantry and 2 artillery. Since they’re French units they can’t jointly attack you alongside another nation. The worst they can do is suicide against you to try to soften you up for a UK or US offensive.
I think in the short run it looks like a bad strategy but in the long run you ultimately deny 5 IPC and 2 minor factories to the Americans (most likely). Those 4 troops that you’re possibly leaving in the territories more than make up for the 6 tanks that America will be pumping out every turn once they land. Since the Americans won’t have factories in Europe they’ll need to spend more on transports at 7 IPC apiece. Without having to spread forces occupying Normandy and Southern France (and possibly moving them back) you can instead concentrate on fortifying Holland or West Germany.
If I’m Axis in my next global game I’ll definitely try it out.