Agreed. The BEF would also have more time to train their forces for the offensive without the pressure on Verdun forcing them to attack early, further increasing its effectiveness.
Why wouldn't the pressure on the Russians and their threats to make a separate peace force the British to launch an early offensive like IOTL? After the 1915 offensives against Russia, the West owes Russia support, especially if the Germans do what Tom B suggests, as they will launch their costly Lake Naroch offensive to support the French.
The biggest problem is that it is very hard seeing Falkenhayn doing this. I might therefore suggest a modified version of this. The POD is there is some sort of friction between Wilhelm and Falkenhayn at beginning of 1916. The Kaiser was so erratic this is clearly plausible. Part of the friction is that Wilhelm has become convinced of an Eastern strategy for 1916.
Despite this Falkenhayn being Falkenhayn goes ahead with Operation Judgment despite Wilhem's opinion. However since he believes his job is hanging by a thread he pays it more attention and avoids "see what you want to see" mode. The result is as of 1 March he orders the offensive suspended and after a week of intense study switches to an East stategy reluctantly and "temporarily''.
Something to note is avoiding Verdun completely and massively redeploying to the east means there is a chance of Entente success at the Somme because there will be much stronger French participation and the French had better tactics than the BEF (borderline faint praise) With a short sharp Verdun they will be forced to commit some strength there they intended for the Somme.
There is the tricky question of whether the change in German strategy causes Conrad to call off/postpone Trentino.
I would also point out if the CP merely take Rovno and Tarnopol they deny Brusilov key staging areas making his historical offensive impossible.
There is also the possibility of mission creep which is what essentially happened in 1915 repeating itself. So what begins as a very limited "brief" offensive could expand into something as ambitious as a Take Kiev strategy.
Lastly there are the Romanians. Clearly their joining the Entente is avoided. There is the question of their possibly joining the CP. However there is a possibility that while they will be reluctant to join outright they may give the Heer the right to pass through their territory which would make it easier to outflank Brusilov and threaten Odessa.
I've read the Falkenhayn-Wilhelm relationship as Wilhelm implicitly trusting Falkenhayn until Romania entered the war. I cannot recall a single instance of Wilhelm having any influence over the military once the war started that didn't stem from Falkenhayn 'asking' for something.
I fully agree that Falkenhayn is a very difficult obstacle to overcome; I was interested in what the results of a different strategy would be, even though it would be outside the conceptual realities of OHL in 1915-6.
Perhaps if intelligence is better and Falkenhayn realizes that further efforts at Verdun past March are pointless he will abandon the offensive, but mission creep and personal investment in that strategy are very difficult things to overcome.
As to the French at the Somme, I understand their tactics improved so much based on the experiences of Verdun, which cemented the lessons of 1915 and enhanced them. So if Verdun isn't launched, the French won't be nearly as skilled on the attack as they were IOTL, though they will be better than 1915. But without Verdun the Germans won't think that the French are committed elsewhere and pull troops out of the French sector on the Somme, which was IOTL THE great reason for French success during the Somme campaign. So the French will do significantly worse at the Somme than IOTL, but without Verdun their overall losses for the year will be lower.
I wonder if it might be possible for Falkenhayn to consider that on account of having a limited reserve in February 1916 (IIRC 20 divisions), which was not enough to attack on both banks of the Meuse river simultaneously, something he writes worrying about in his memoirs, could have potential resulted in a strategy of inflicting losses on the Russians, who he already knows cannot do well against the German artillery train, to economize his commitments AND force the Entente into hasty action on the Western Front like he hoped to do with the Verdun offensive. A winter campaign in Ukraine is not like the situation in the Carpathians in 1914-5, so he could launch a series of limited offensives to tie down the Russians (though I realize he thought they were already crippled from 1915), potentially bring the Romanians into the war on the CP side, and maybe force a separate peace again. It would also potentially open up Ukrainian farmland to CP harvesting.
Also the fear of Russia making a separate peace would conceivably force the Entente to attack in the West before they were ready, which Falkenhayn already thought would be a disaster. Of couse that would require him to not be disenchanted with the idea of being able to force the Russians out of the war, which is why he went after the French in 1916.
Edit:
What about poison gas? The French had gas masks that were able to deal with Green Cross in 1916, so it made little impact upon its debut. But the Russians were a generation behind on gas mask technology. So Green Cross could make a much bigger impact against the Russians if used on the offensive and with an artillery scheme devised by someone like Bruchmüller, who IIRC had already been the Eastern Front's artillery expert.
I know that Franz Josef had banned gas use by his forces, but I'm not sure if he forbid its use on A-H force's fronts.