Given that the US has nukes, why have any other military at all? You could ask the same China.

Conventional military and geopolitics are relevant for everything that you wont launch a nuke over. Without conventional power, any nuclear power can be bled to death with 1000 small cuts nukes cant stop.

I disagree that the decision makers in Russia who made the decision for war were motivated mostly in their own hold on power. If they were, they probably would not engage in such a risky business as a major war. Power is more secure in a stable political environment. To take one example, decision makers in Germany before the first world war had no illusions that a major industrialized european war was risky for the political order and its outcome was very uncertain. One reason why Germany refused to expand conscription was the fear the aristocratic class would lose power in any new citizen army with mass conscription( which in fact, happened).

So even in an autocracy this incentive problem still exists. Democracy certainly reduces the incentives for decision makers to go to war over security concerns but even in a democratic states these cross cutting concerns of political stability and economic well being could find themselves at odds with having to ensure the security of the state that makes such prosperity possible.