Interesting lines of thought. One question tough: why do you not think it makes a good second strike weapon. I thought that was exactly what it is.
Pretty much because of the reasons everyone else here is hung up on, how much seabed you can vaporise and how many fish can you can fry.
Because in a nuclear war your own ICBMs and SLBMs should have neutralised your enemy's main silos and airbases and knocked out their first or second strike forces. Assuming you can sustain any kind of bombardment beyond the first couple of hours into the following days or weeks, irradiating your enemy's coastline is probably the least of the strategic goals when several hundred megatons have already been expended while your Kanyon has taken 5 days to finish off whatever might still be standing.
As I've said, blackmail as first strike is only possible if you gamble your enemy won't just fire up its ICBMs and seriously outpace you before your Kanyon near enough its target.
I really can't see any logical reason why this weapon system or its parent submarines should exist given the existing missile technology (unless you assume a 100% kill ABM system is around the corner). It seems a very expensive blind alley. I still think its a disinformation exercise and that those 'leaked' plans are just propaganda while the real purpose of 09851 and 09852 is something much more mundane and Status-6 may well really be some kind of nuclear-powered reconnaissance USV or something along those lines.