I love the idea, in principal, but I think it's impossible in practice.

A good strategist makes the outcomes of individual battles predictable. That makes it terrible for unit players.

I used to play Planetside 2 with a very organized group. Winning was fun at first but you were ultimately a cog in a well oiled machine so it got old fast. It probably got old even faster for the other players who were just trying to play a regular fps.

It's what Eve Online was in better days.

The timescale between shooter and strategy layers sounds too great for that to work. Imagine playing Civilization like that. You build and set your army to attack the enemy but then you have to wait for the hour long shooting match in Battlefield to resolve. Sounds as exciting as playing multiplayer Civ where you have to wait for the others to spend as long resolving their turns as you did yours.