Mods are nice but usually have poor QA and I usually avoid them. Also, I would rather pay $10+ for a a 1943 start date than new focus trees for, say, the Balkan countries (which are nice, but don't matter too much unless you actually play those countries). Also, I would rather have one well made mid-game start than a lot of not so good ones. Also, March of 1943 is the last moment the Axis could hope for a "draw." Later dates will only offer a " tactical" challenge for the Allies, while ones before Stalingrad will be somewhat similar to the 1936 start.
Now, it is true that if you would want to make a 1943 start you need to know the front lines and order of battle. But this is all well documented and even can even be found on wikipedia without access to actual historical resources. The trick is, though, to pick a good date when things were not very fluid, which is why mid March is better than, say, January.
Your raise a good point about templates. The current system works well in the sense that it gives benefits to countries gaining experience early by participating in the SCW or sending attaches to China. But the end result of having all AI countries use 7-2 divisions is about the same as removing the substructure entirely and just have "infantry divisions," etc.
A mid-game start would thus require some choices to be made. The most important of which would relate to the peace conferences, which I don't think can be fixed in a meaningful way unless there is still something to do afterwards (and there are plenty of interesting options to explore, all of which would feel more relevant than a 1930's US civil war or a democratic Japan). But there are also many others, like whether to keep the template system, perhaps reworking it to better represent historic formations, and how to implement late-war navies, which cannot be built starting in 1936 given the limited amount of steel that is available.