The alternative wasn't a Tsar. The alternative was a liberal representative democracy under Alexander Kerensky. Lenin took over before the planned elections for a Russian Assembly and kicked off a civil war that resulted in one of the worst governments in modern history, while Kerensky ended up teaching undergrads at Stanford.
I've seen Lenin, in his tomb, back in the day when the Russians thought it was cool, and brides and grooms would make a stop there between wedding and reception...
I think we should keep the old boy right there, where we can watch him.
Seriously, I don't think it's good for a country to bury its history. Let his body stay where it is as a reminder to the Russians to "never forget" what happens if you let your government get out of your control.