There's no guarantee that what replaces Putin is going to be more Western and not reactionary. For every Russian that is cosmopolitan and globalist, there's a dozen Russians in small villages that are True Believers and will see this foreign pressure for what it is: replacing a Russian president that, at least in their mind, they put there.
Even if you assume that it's going to be a democratic and Western government that rises from the ashes, I think the timescale for this is in years, not months, and I think that the impact on the average citizen in The West is going to be massive while we wait that out.
I paid north of $80 last night for 18 gallons of fuel, and it's only going to get worse. In Europe, they're staring down the barrel of a significant energy crisis next winter. Energy is everything: it's fertilizer and it's heat. And this is all on the tail of record inflation and a shaky economy.
Hot take: I think this is going to backfire and we're going to see destabilization in Europe and America before Putin is ousted. War tends to be a boon for the economy in the West, but I see good reason why this time could be different.