You raise an interesting thing to ponder. Leadership BEFORE the crisis might have been possible. Once the crisis was at hand, I can’t see it as a workable strategy. Nicholas II was a weak man, and defending the Motherland successfully was imperative to justify his rule. Cousin Willie peltered Nicholas with patronizing “advice” and arrogated personal seniority if not outright superiority. Then there is the problem that if your foe mobilizes and you don’t, your military will not be able to catch up — your goose is cooked (someone above mentioned that Wilhelm pushed Nicholas to stop mobilizing — as if that would not have completely derailed archaic Russia’s ability to get back on track). The Russian military, on which Nicholas depended to stay in power, would have ousted him rather than take such a risk. (For how unilaterally not mobilizing works in practice, see Trotsky’s “No War, No Peace” gimmick after Revolutionary Russia declared it was leaving the war — the German Army ate Russian territory like candy).
Asquith and Britain did not have the personal dynamics, but the geopolitical calculus would have been: if Britain does not enter the war, France and Russia will be quickly defeated and collapse, leaving Germany to turn its wolfish eye, and all Europe’s resources, on Britain. Even without an invasion, Britain’s economic and political standing would plummet.
I always wonder though if Germany really wanted the British Empire? Yes, they had no use for the French, but I think they at least respected Britain. They saw Britain more as a rival than an enemy.
If Germany had defeated France. Note I’m assuming no UK participation. I can’t see Germany occupying France, or any annexation of French territory. It already had a restive Alsace-Lorraine. (Which baffled the Germans did these people not speak German? What’s wrong with them?) They may have grabbed a few French colonies. I think Germany would have preferred a return to the status quo in Europe, a status with an acknowment that Germany was the big dog. I think they would have been busy propping Russia up trying to keep Nicky or some Romanov on the throne.