Speaking as someone who has not actually done this, I don’t like the idea of it because if you buy the complex, you get 3 infantry per turn only one step closer to the fight for the price of 5 infantry. That loss of 5 infantry alone increases the risk of the Allies teaming up to develop a forward position against Germany in the early stages. An example would be the UK landing heavily in Karelia on maybe UK2 or UK3, America landing fighters there, and Russia reinforcing with her West Russia stack and fighters. Another method that could work is the UK using a few Mideast troops to take Ukraine and again have the US and USSR help to hold it. Any of these scenarios makes it more difficult for EE to be held.
The fact that you’re building units in EE means you are building less on Berlin and Rome. In the later stages of a game, you’ll have to keep extra units behind just to hold Germany against an amphibious assault or to sufficiently deadzone Western Europe. By that time, you’ll be wishing you had the 5 infantry back because the EE complex won’t be any use to you, and at some point, it will be captured.
While I don’t always view losing EE as end game for the Axis, I don’t think it is a clever tool to draw Englishmen to their deaths either. A player should be able to manage deadzones and if Germany deadzones EE, then the Allies won’t go in heavily, they’ll go in with just enough to get the job done and get paid for the territory.
I don’t think that Germany would be that successful building 3 inf plus tanks every turn. Naked tanks like that will give the Soviets plenty of strafing material. Don’t get me wrong, Germany should add some tanks to their starting stack but they need infantry to hold against the Allies long enough.
In theory, you might like the idea, but try it in a game with a veteran player and I think your opinion will change.