Whatever Kasparov says or does in exile is quite irrelevant in Russia. This is how actual Russians think:
"He's not even in Russia, what does he know."
I don't know why Navalny returned to Russia after being poisoned and nearly killed by Putin's thugs, but it was a very brave thing to do. It makes no sense.
As close as I can tell, Russians tend to be very fatalistic. It's never been a happy place. It's cold, the state is corrupt, life is cheap. But people have a strong personal need for justice, to find those guilty and make them pay. But the state won't deliver justice, so you make a stand, and life is cheap so you take risks and double down. Hence Navalny, hence Litvinenko, hence all the journalists over the years who reported until they were thrown out windows or gunned down in public. Incredibly brave, I only wish the bravery led to real change rather than a neverending Greek tragedy.
It is because as a person you feel nothing else can be done. So you do the thing that you can do, knowing that probably it can't change much but... what else can you do? Doing nothing like everyone else? From the outside it looks like madness, but when you are that person it seems like keeping your integrity and being able to look in the mirror.