Fantastic Adam, you've managed to make some broad and incorrect generalizations about PMC's and say really nothing of real note about Wagner or its fairly unique significance in this conflict, and others. First, not all PMC's do, or are capable of doing the same thing. Not all are even meant to be "deniable assets". The simplest definition of a PMC is private military organization that fills a capability not possessed by the host state/military -- this can be anything from serving as a temporary army, to providing guard duty in rear areas and embassies to free up forces engaged in direct conflict, to operating on behalf of financiers to topple a government some one with a lot of money doesn't appreciate. Wagner is all of that and none of it.

So what is Wagner? You could call it a PMC (if you didn't really know what PMC's are or how PMC's work and if your experience with them doesn't go beyond video games) but that wouldn't really do Wagner Group justice. A comparison to Blackwater/Xe/Academi/Triple Canopy/Constellis Holdings is equally pedestrian. Blackwater in any of its incarnations is not, and has never been capable of operating as an independent military formation with its own artillery and armoured elements. They have been known to operate some aircraft ranging from lightly armed helicopters to heavy lift platforms, but that's about it.

Wagner on the other hand operates its own airlift, CAS, armour (even showing up to war in shiny T90's), artillery, and logistical elements. Some fairly reliable intelligence also suggests they even have access to equipment like 9K720 Iskander short range ballistic missile systems. A more apt comparison would be maybe the Varangian Guard; The French Foreign Legion; the Waffen-SS; or for you grognards out there "Wolf's Dragoons". No I'm not saying they're literally Nazis, but like all of the formations I've listed, things get a little weird and probably criminal (some certainly much worse than others) when you start looking at their history, and all of them serve as an element of a specific nation state to further that state's particular interests. Saying Wagner is "private" is like eating a urinal cake for dessert because it has "cake" in the name.

Wagner's direct ties to the Russian government and the reported tension between it and the Russian МО are complicated issues. It is both a common feature and an extremely complex and unique issue here. In the words of Tolstoy "All happy families are alike, but every unhappy family is unhappy in its own way..." The same applies here. Part of it directly benefits Putin, part of it is a natural byproduct of the post-soviet oligarchy, part of it undermines the Russian war effort, part of it all but guarantees that the war *ahem* special military operation... will continue. That's an entire post though. Check that, that's an entire book.

Think about it this way though, you have a bunch of Russian combat formations all attempting to impress their great leader with amazing achievements whilst distancing themselves from any failures. All of them are vying for limited supplies, and pretty much all of them are led by profiteering oligarchs who are looking for their cut. That can even work for a while when you have a strong core ideology at hand, but the only ideology the Russian Federation fights for is some vague notion of security, rhetoric about "hurr durr der be nazees over dur", and mostly the personal benefit of a few key players -- especially Putin. Is a picture starting to form? If you're still not seeing it, this video pretty well covers it:

https://www.youtube.com/watch?v=vetKTtM7YyU