I agree with you that everyone was happy to make Beria into the ultimate bogeyman, in a large part to distract from their own bogeyman like activities. However, he was the only one of the top post-Stalin leadership who was executed rather than simply marginalized, which has to mean something - for whatever reason he must have been thought of as a higher risk if left alive. Or maybe he was the one person no one could compromise with. As has been pointed out in this thread, being feared is all fine and good but it's not enough on its own.
It is an interesting question how long before the suicide becomes public knowledge. It would be a fairly narrow circle at first, so I think it stays under wraps during the war. But if there is some version of OTL de-Stalinization afterwards, it would be awfully tempting for whoever is running it to throw in something about the "horrible tyrant Stalin, having led the socialist state to the brink of disaster, did not even have the courage to be held accountable by the party... " and so on - you get the idea. And of course the inevitable whispered conspiracy theories about who really pulled the trigger.
I find it very difficult to say whether Stalin's death would result in the USSR doing worse or better in the war. I think the transition itself would be reasonably smooth. It has been pointed out that rule by committee is not very effective, but the Bolsheviks won the civil war through rule by committee; Lenin was there of course but he was much more primus inter pares than unquestioned ruler in the way Stalin was in 1941. Some figures in the Defense Committee are bound to end up more powerful than others, I think that's the nature of all committees, but nothing focuses the mind like an existentialist struggle, in 1941 and 1942 they should all have a clear understanding that if the Germans win, they will all hang together.
