>Russia was ruled by tyrannical czars for centuries before Communism - does that mean the actions of Communist leaders like Stalin were really the czars' fault?
Absolutely yes, a thousand times. Maybe Nicky wasn't responsible for the colors Stalin picked for his office walls, but most of the important, nation-wide decisions were obviously affected by how (dismally) Nicky ran things.
>For how long can you blame the czars when they're no longer in power?
I'd say a very long time, probably centuries. I'm sure there's a PhD thesis or other publication somewhere estimating how long each economic/social policy impacted the country. Note that this isn't the same as saying "meh, we found it like this, let's not do anything".
>And who does it serve?
Anyone who's interested in learning from history and not repeating mistakes from the past?
>It seems to me blaming the long gone czars mostly serves as a distraction from corruption in the successor government.
It seems to me blaming the successor government mostly serves as a distraction from the very real, very recent despotism and absolutism of semi-medieval tsardom.