My main point is 055 is already playing the same role as Kirov.
They're not.
055...is basically an overgrown destroyer (or Ticos for the matter - they aren't real cruisers nor ever were), but, more crucially, it's a fulcrum node (capacity and capability multiplier) of a networked fleet of other LRSAM combatants.
Nakhimov(talking about Kirov which dates to the era of the original 051 class is essentially pointless) is essentially a one-ship replacement of a deeply networked fleet for a navy that can't afford to create one.
Very long range anti-air missile of same weight class, check. Very long range anti-ship missile that can reach carriers, check.
It's honestly almost impressively simplistic. 052D claims all the same boxes - isn't it an even more impressive example?
But you're looking for the wrong checkboxes in the first place.
First, Nakhimov is basically a replacement of Burke (or 055/052)
grid, not of single ships. In part it does it relying on its sheer size (it's after all carrier-level tall, with a correspondingly high placement of sensors and datalinks).
Then, it has the largest airwing for non-carrier combatants - which is actually known to include AEW helicopter(s).
Second, it is resistant even in situations where there is no reliable 3rd party Shared situational awareness(SA)/targeting data environment (especially low-altitude coverage) in the first place, because of an unreasonable amount of self-defense firepower (CIWS, TDS).
Third, it's arguably the only ship in the world that can actually be expected to take hit(s) and fight (Moskva's
impressive DC effort undermined that point, but let's talk about the ship itself for now). Again, to some degree mitigating mistakes and inherent unavailability of US/China level external SA to 2nd tier navies. It's big, armoured, and well-duplicated.
Fourth, it is unlimited in tactical positioning (nuclear propulsion).
And only then do we come to "very long range missile that can reach carriers". These are honestly a lesser part - not because her hypersonic/land attack cruise missile array isn't impressive per se, but because all Russian VLS frigates and SSGNs have the same thing, just in smaller numbers. Just a big part of the squadron salvo/strike, nothing more, nothing less.
055 superseded Kirov's role while being 2 weight class below and that is remarkable.
The end result is that if you add a single 055 to a Russian frigate/carrier squadron (let us assume for our small mind experiment their comm links can talk to each other), you still get the same 2nd tier CSG which half a dozen other nations can do. It's painfully limited by radar horizon and the weakness of other units - which both need protection and don't add too much to 055s own life expectancy.
1144M impact for such a second-tier CSG is transformational, as it allows a second-tier group to fight well above its potential.
(to be fair - to 1st tier one it simply won't be able to add anywhere near enough oomph to justify its cost, limiting its practical value to its 160 main cells - here the 055 criteria works).
In PLAN terms - imagine a CSG made out of Liaoning, 2-3 upgraded 956s or 052Bs, but without most of the Chinese air and space ISR, data relay, and datacoms, as well as a directly worse carrier (same hull, worse shape, worse/outdated electronics, dated aircraft).
This is what you're working with.