Making sure every country on earth has nukes is way more likely to cause nukes to be used than beating the russian army out of Ukraine.
First -- Do his nukes even work? Or have they been replaced with cardboard "Nuke Go Here" boxes?
Also -- What's Putin going to nuke? He can try some battlefield nuke, and then have his army march through it? That's assuming that his troops have more than a week of training for "marching through a place we just nuked" Or maybe he'll nuke Kiev? I don't think that'd make much difference in letting russia gain ground. Or maybe Putin is planning on nuking Rotterdam because of the F-16s?
Nukes may make china and india stop supporting him, they may provoke more retaliation from the west. But nukes certainly won't change much unless the plan is to just glass the whole of Ukraine, in which case I'm pretty sure that France or England may accidentally glass Moscow even if the USA doesn't.
Currently, it seems the US would rather glass London and Paris if that happened.
And anything _less_ than glassing Ukraine is unlikely to change Ukraine's behavior or materially affect the special military operation's progress.
Hypothetically, if Ukraine has a breakthrough after a massive collapse of the russian army, nukes will prevent Ukraine from going all the way to Lubyanka Square. But there's no way to use nukes to help the russian invasion any more than a shotgun will help with colon cancer.
If there is one thing that this war has shown us, it is that a country's security is in its own hands and a Nuclear Weapon is the difference between being invaded and conquered (ex: North Korea and soon to be Iran).
No one can control what will happen, but the simple reality is that allowing Russia to push a war of aggression out of fear of a nuclear attack endorses the idea that anyone with Nuclear capability can do what they want. China, India, etc can annex or invade and no one will stop them because it might trigger escalation. That reinforces the need for less powerful nations to pursue nuclear capability. Those smaller, less stable nations will be more likely to lose control of a nuclear weapon.
It's a catch 22 so we might as well try to err on the side of stopping wars of aggression. The other path is open for the cowards who would rather bend the knee or look the other way until aggression knocks on their front door.
And Europe will suffer greatly if a resurgent USSR is allowed to grow unchecked next to it. (Not even speaking of the millions of people who will suffer under its authoritarian rule.)