I’m certainly in favor of broadening criteria for granting asylum, but I wanna say that realistically, for the US and Canada to be viable options for people fleeing Ukraine and Russia, the US (and possibly Canada, not sure) would need a complete overhaul of the asylum and immigration system in general.
Ukrainian airspace is completely closed to all civil traffic, and people fleeing the country need to first cross one its western borders by car/train/foot. And that immediately runs into the Third Safe Country Agreement. Not that the US Embassy in Kyiv has any visa services at the moment anyway. Ukrainians seeking entry to the US could have gone to the consulate in Warsaw, which is currently designated as the primary one for Ukrainian citizens, but it very specifically says that non-immigrant visas for refugees don’t exist; for an immigrant visa, you need to be otherwise eligible for it; and to get any other non-immigrant visa, you need to prove the lack of immigrant intent, which is basically impossible right now.
In Russia, it’s less bad, but the gist is the same. Russian planes can’t fly to EU and US, and European and American planes can’t fly to Russia. So far, you can connect via Turkey, but no one knows how long this is gonna be available. US consulates haven’t been providing visa services for several years, and I think it’s been a year now since all consular services even for US citizens in Russia have been suspended; only the diplomatic mission remains. It used to be possible to apply abroad, but unlike Ukrainians, Russians need visas to go to the EU and apply there, and multiple EU countries have already stopped issuing any visas to any Russian citizens, regardless of where they apply. And even if one manages to get to a US consulate, the caveat “you’re not gonna prove that you want to return to Russia to anyone” still applies.
And the non-immigrant visa thing is the key. You can’t apply for asylum while abroad; at best, you can do it at the border crossing, but even that is more difficult, compared to first crossing the US border, and then applying from within the country. So basically, the only way to get asylum in the US is to lie on the visa interview and at the border crossing, and these days, the lie would be so obvious that no one would believe it. Theoretically, you might apply for humanitarian parole while abroad, but it can take years, even though it’s partially designed for emergencies...
tl;dr: to make fleeing from Ukraine and Russia to the US possible, you need a massive overhaul of the entire immigration system, and I doubt that it’s possible without supermajorities everywhere.