Pulling troops from other areas
They wouldn't have to do that, or are you suggesting they left a large area of the front open with no front line or reserve troops and the British didn't take advantage of that? No, the troops were there.
The idea is to minimize the time that they're in the kill zone.
OK, they're in the killzone for 10% less time. It leads to no change in the amount of casualties they take. Now how did that change the war? Hint: Germany still loses.
To my eyes, World War 1 is one of the rare times that a few subtle changes COULD change the tide of the war.
You are hilariously naive then. For every small advancement you still needed to back it with hundreds of thousands of troops. Against hundreds of thousands of troops. A few change here and there after war has already started isn't going to greatly affect that.
they would have achieved a breakout.
One, they would have achieved one breakout. And then dug in when coming up against the reserve forces and started the process again, this time against people prepared for it. Again, not making or breaking the war here, simply changing lines and dates slightly.
and success there would lead to more influence
Until they overreach their knowledge, and again based on the premise people are listing to the guy in uniform with no record of existing and talking about time travel.
Not having to pay in blood for that knowledge is a tangible advantage.
You are forgetting ground troops as recon were a thing, and how incidental the air war of WWI was. Nothing about WWI air forces gave a clear ability to gain ground like it has later on. So Britain and France use better fighter tactics and barely achieve air superiority, now what? Bomb Berlin? No, don't have the range. Take out trenches? Armament of the aircraft is weak enough that's it's far more cost efficient to hit it with artillery. Better recon? OK, so you know where the enemy is and if they're going to make a push, but unless you have troops to commit there all you do is get advance warning that you're going to lose ground. Maintain secrecy of moving troops? Still not a guarantee since there are other ways to find that out that were used.
Every change that led to the eventual outcome of the war was implemented on the fly.
But using technology and knowledge that everyone was familiar with.
The entire focus and structure of an infantry division, for example, changed from large bodies of troops, to small unit tactics
That's a simple dividing men up further. That's not overhauling or building a new factory to make things a different way, or training someone to make things a different way, at the cost of production already going on. You say saving a few lbs of steel would be really important for wartime production, so how would cutting production down or stopping it entirely even for a short time not be an important factor?