I don't know about Battlefield, but the other four you've mentioned all contain campaign modes in which the player has to complete specific objectives in order to move on to the next level. These objectives frequently involve puzzle solving (as opposed to the objectives that are of the "kill X number of enemies/clear the area to progress").
To use a famous example from one of the series you've mentioned, The Silent Cartographer from the original Halo. You have to locate and deactivate the security system as well as
survive. There's navigation of an environment, and working out the required sequence and appropriate location, involved as well as just brute force shooting. To use another famous FPS example that I can think of - Goldeneye on the N64 contained plenty of puzzles, usually locating and destroying or installing items.
Not sure if you are assuming people only play the multiplayer versions of FPS games, wherein I assume tactics and strategy are more prominent, but it's not the only available way of playing