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Of course it's not a "desperate war to the last Ukrainian." They're volunteering for the benefit of the necessity of depopulation, because out of love they know that the whole world is suffering from over-population. Lol.
I don't think that Biden will be able to force a draft on Americans. And the Nato countries don't like the idea at all. This means that outside of a few strays that go to fight for Ukraine, all Russia has to do is keep on killing Ukraine soldiers. The problem for Russia is, when all the Ukrainians are dead, there won't be anybody left to surrender.
Consider Dresden in Germany in WW2. They thought they were safe, being rather far from Berlin, and near the Czechoslovakian border. But they got bombed right off the map, and now Czechoslovakia is even gone.

1. Ukrainians fight for a variety of reasons. These include patriotism, money, their land, their families, their freedom and many other as good or as bad.
2. US is unlikely to send soldiers to Ukraine but certainly would not ever send conscripts. You are spreading fake information and trying to scare people - I guess some of them are stupid enough to believe such a thing.
3. Considering Germany after WW II is precisely why Ruzzia needs to be stopped here and now, to avoid them spreading their influence over half of Europe. Cold war was extremely costly, only a fool would want to repeat it. The cheap and smart alternative is to drive Ruzzia back to their borders while it demilitarises and destroys its economy itself in the way so that the do not come back for more.
And, again providing biased information. Czechoslovakia is not "gone" it is two states Czechia and Slovakia, which by the way have very good industrial bases, an educated population and growing economies in the context of the European Union. You know why? Because they are free from Ruzzia stealing from them and governing from Moscow - does this ring a bell to you???
You forgot the biggest reason why Ukrainians fight.
4. They are stupidly believing that they have a chance, just like Americans listening to THEIR government and media about Ukraine think Ukraine is winning. Dying futilely for "patriotism, money, their land, their families, their freedom and many other as good or as bad" aren't good reasons to die. I mean, nobody will be there to take care of their families once they are dead. And they certainly won't take their land and wealth into the grave with themselves. Zelensky certainly won't help. He'll be just as gone as they are.