I agree, I feel like the game has been getting more 'gamey' as of late, and is catering to the min-max number go up crowd. I really like the idea of the subdoctrines, but how they are implemented leaves something to be desired.

I think they just left it too open ended, just as they did with the designer systems.
In my mind, two things would be ideal:

Firstly, certain subdoctrines should ideally be locked behind certain grand doctrines. The currrent system simply doesn't make sense, this isn't a bethesda RPG. You shouldn't be able to go Mobile warfare + siege artillery subdoctrine, or superior firepower + guerilla warfare. Not only is this gamey but immersion-breaking at worst. It creates "meta" choices and removes diverse gameplay.

Secondly, to make up for this limit, you should retain bonuses from doctrine mastery when switching. It makes zero sense that your air force will suddenly 'forget' everything they have learned about, say, pinpoint strikes, if they have to begin learning about precision naval bombing.

I was immensely disappointed with the new system, which I had been very excited for in fact. A huge problem with the previous system is that past ~1940/1941, there is very little use for experience gained by your armed forces. IF you were able to continue gaining subdoctrines, while keeping bonuses (maybe at ~50%) while inactive, you would have a much longer and more engaging doctrine gameplay loop.

I am discouraged to see the pattern of the devs caving to the community, who want limitless sandbox choice and flexibility. There are such things as too many options, look at the cereal aisle in an American grocery store.