Membership can come quickly: Finland became a member rather swiftly. I figure most members would want the war the end as soon as possible because it’s a moneydrain. European members are not eager to prolong a war just outside their borders.
The situation is different for the US of course. I don’t agree with you on Russia: A prolonged war is in the best interest of the US as it weakens Russia over time. Their current economy and sanctions don’t allow a long-term “military operation”. Furthermore China can’t rely on a weak ally if shit hits the fan in Taiwan. Ukraine is also a prime example on how willing the US is to support allies in a long-term proxy war.