I wrote an article for a newspaper in Phoenix, AZ right after the attack in Beslan. I opined that Putin would maintain his power-base in Russia by doing exactly what you listed against the Chechen Islamists. Putin did exactly that and the mass of the Russian populace voted for him and kept him in power at every single instance.
That has always been the Russian answer to enemies both foreign and domestic. And they see the Islamists as their primary enemy.