It's not exactly true, the western front was far from static until the battle of the Aisne and the Race to the sea, and it opened up again in 1918. Meanwhile the eastern front was quite mobile.
Of course this make it even harder to represent as the game would have to be able represent both the static and mobile phases.
A good WW1 game should also represent the mobilization and the time it took. Also a big part of the stalemate on the western front was the time it took for the generals to learn what happened on the front and for their instruction to be received, preventing exploitation of successful offensives before the enemy could counterattack. That's not something that HOI does.
Not at all. If mobilisation of manpower is more tightly locked, the first phase of war is ok to represent with just low troops density,band low level of entrenchment possible. Then, you can add several techs, or doctrines, or techs that get massive bonus to entrenchment and increase defence value of light artillery.
Then, by 1916-1917, tactics, techs, ex, should get unlocked, that would boost breakthrough, and maybe even reduce entrenchment level possible, and front will start moving again.
The greatest fault of all WW1 mods I've seen is the fact unit stats are so static. Now, this can be said to be true in WW2, but for WW1, this shouldn't be so.