A useful analysis ! There is another way of looking at it; that Russia's security concerns are valid, and that Biden thinks wrapping himself in the Stars & Stripes and portraying himself as a wartime president will improve his domestic ratings in time for the mid-term elections.
A lot of Americans think it'll be like Serbia, Iraq, Afghanistan or Libya; a proxy war in a far away place with just enough US dead to make them feel patriotic, but no risk of actual damage to the US homeland. They forget that Russia has a proud history literally built on fending off wave after wave of invaders (from the Golden Horde onward), and they are tough and imaginative fighters. While they probably can't win against the US, they can make sure no-one wins, and can probably hold on for long enough for China to join the party. I just really hope it doesn't come to that !