Inevitably Russia will defeat the Ukrainian army while suffering heavy losses.
If it were that inevitable, it would have happened by now. Russian corruption and ineptitude is interfering at every level, and the resources they have left before that corruption skims off the top are becoming even more scarce.
The US won't send a replacement army, neither will European countries.
Currently, the Ukrainians don't require an army, they require weapons - and we seem to be stepping up in that area. As time progresses, I'd agree it seems highly unlikely that the US will send troops should they be required, but the EU is building an armed response of its own, and it might decide that there's a need to show that's not just a paper tiger. I'm not saying it's likely or soon, but I can see a situation where that might happen.
There is no guarantee that a future US president will.
But, equally, no guarantee that they won't, which puts pressure on Russia to try to achieve its goal soon. If - as seems quite possible - Trump's mismanagement of the US results in a boost to the Democrats in the next election it's likely that the next President's administration will support Ukraine. If enough change is apparent at the midterms, next year, that might be enough to shift the sentiment in the US.
So why not avoid these losses and agree to Russia's peace terms?
Because they don't want to lose more territory, they don't want their kidnapped children to be brought up in one of the scummiest countries on the planet, because living as third class citizens in a shit-hole like Russia seems like a worse prospect to them than dying on the battlefield. Russia doesn't want 'peace' it wants capitulation and subjugation.
By the way, the side that is losing doesn't get to demand a ceasefire unless it agrees to the other side's terms, in this case withdrawing from the four regions and ending military aid.
Your assumption here is that Ukraine is losing - that's not apparent to anyone except you, apparently.
Russia was not aggressively expansionist at the time when those countries joined NATO. "No participating State will strengthen its security at the expense of the security of other States." - The Charter for European Security, 1999.
Russian troops entered Chechnya (the second time) when Putin was took over as acting President - that was nothing to do with EU expansion, and years before the fifth - and largest - EU expansion. And, even if it was related, it's not Putin's business if two countries that aren't Russia want to agree to something. When it comes to the NATO expansions, the post-cold war expansions was a direct result of Russian hard-ball tactics at the time - Russia threatened repercussions if their former 'colonies' didn't toe the line, and so Bulgaria, Czechoslovakia, Latvia, Lithuania and the rest all jumped into NATO. Russia was attempting to create, functionally, puppet nations around itself by threatening them into compliance.
EU expansion, entering into a free-market, free-movement, free-trade co-operative, does nothing to jeapordise Russian security, it jeapordises Russian ambitions at empire building. The countries that joined NATO did so not to compromise Russian security - which wasn't at risk - but to protect their own from imminent Russian aggression.
Based on the above OSCE principle, the invasion, and those you have listed also, were preemptive because Russia's security was threatened, by NATO expansion and meddling.
How? That's always been the Russian stance, and it's bullshit. I find it hard to believe that they believe it, but even if they do their belief doesn't make it real. We don't need to surrender Ukraine because they don't understand, we need to explain it terms they will, and if those terms have to be put in writing alongside their formal concessions and withdrawal from the country they've invaded, so much the better.
O.