Should Western countries take in Russian men fleeing mobilisation?

I think I speak for most here when I say that Russia is 100% wrong to have started its insane war against Ukraine and I hope they lose. Spectacularly.

But for myself, I think the West might be missing a trick with regards to Poo-tin's recent "partial mobilisation" and the subsequent mass-migration of Russians (mostly men) to other countries. More specifically, I think Western countries should offer resettlement visas/asylum to Russians fleeing mobilisation and also their families. Although some might disagree claiming that Russians as people are at least in part responsible for their country's misdeeds, I do not believe that "Russians" can be grouped so easily. As far as I can see, there are three "groups" of Russians at least as far as this conflict is concerned:

• Western-outlook Russians who are horrified by this, they cannot protest the war as all kinds of protest have been basically banned in Russia and there have been stories since mobilisation that men arrested at illegal protests were sent to the front lines from the police station. These people legitimately did not cause their own difficulties and should certainly be considered candidates for asylum in cilivised countries.
• Apolitical Russians. According to the Youtuber NFKRZ in one of his videos, when Putin came to power in Russia he basically offered the Russian people a "deal" that if you, as a citizen, stay out of politics, you will be comfortable. Given what happens to people who are political, like Alexander Navalny for example, it's reasonable to see why so many Russians up until now have taken that.
• The imperialist, hyper-nationalist Z assholes who support everything their government is doing ... but now that they're given the chance to go to Ukraine and personally show those so-and-sos what for, aren't so keen. 🙄

Obviously, if Western countries were to give asylum to fleeing Russians, we would like to prioritise the first two groups and keep group 3 out as much as possible. Obviously, that would be difficult, but I still think there would be all around benefits for Western countries, Ukraine and some of Russia's other neighbours if Western countries were to offer resettlement visas and asylum to fleeing Russians. My reasons follow:

1. Every Russian that flees is not only not going to be in Ukraine murdering Ukrainians, they're also not going to be working in Russia, paying taxes to the Russian government or spending their money in the Russian economy.
2. Many of Russias neighbours that have visa-free access for Russians have suddenly found themselves with a sudden and rather large surplus of Russians, countries like Gerogia, Kazakhstan, Armenia, Turkey even Mongolia. Some of those countries have a rather poor history with Russia like Georgia and Kazakhstan, and in those countries it can be somewhat anxiety inducing for geopolitical reasons, not to mention day to day reasons like rising rents in Tiblisi etc as there is a sudden surge in demand for apartments. Allowing Russians to leave those countries for Western European countries could provide a sort of safety valve for the countries just mentioned. It would also make room for more fleeing Russians in those border countries.
3. Many European countries are in a demographic winter. In countries like Germany and Italy for example, the locals have basically stopped having children and absent mass immigration, their demographics are so far beyond terminal that it beggars belief.

Essentially, I'm suggesting a win-win-win-win. For the Russians who get to live, the Ukrainians who have to deal with a smaller and weaker Russia, Russia's border countries that get relief from their sudden surplus of Russians, and for Western countries otherwise in a state of demographic collapse.