I am sure there will be a lot of comments pointing to Azov's history, paraphernalia, alleged statements, etc., to support Russia's claim.
I am going to remain neutral on that claim in this answer though in order to answer the actual question as it has been asked
Is there any value for Russians in completely eliminating the Ukrainian resistance at Azovstal, Mariupol?
There is little reason to do if the Azov Regiment (successor to Azov Battalion ) is, in fact, a neo-Nazi organization, as the Russian Federation claims. If Azov members indeed do hold neo-Nazi views, the best way to expose them would be to arrest them and to conduct interviews with them after enough time has passed that the passions of their convictions have diminished.
This was commonly done with former SS and Warmacht officers arrested during WWII. And it gave great insight into how the Nazi Germany became a Nazi regime.
If, however, Azov being a "nazi" organization is a ruse used by the Russian Federation as a yet-another excuse for its unprovoked war of aggression against Ukraine, then the Russian Federation would greatly benefit from killing them all.
If they can't be interviewed and they can't show who they are to anyone, not even to any professional psychologists or interrogators, then Russia can attribute any views or opinions to them. All it has to do is manufacture some pictures or other "signature unclear" type evidence.