I think the easiest to imagine is the USMC winning the fight with congress over large calibre fire support. If they could convince congress or the navy that something larger calibre than the AGS or Mk 71 is needed a dedicated fire support platform starts to look better than reactivating battleships between their age, crew requirements and the lack of need for armour and mid calibre guns on a modern fire support ship.
Now, whether this would be a true monitor is questionable given that it would have to be seagoing, and that there would be a large temptation to add significant air defences to it making it more of a modern battlecruiser than monitor in design...
In terms of a POD you might not really need one, could still happen given the right combination of failures in the Zumwalt Class and missions required of the Marine Corps. If it really must be AH as opposed to predictive though, I'd think giving the Iowa class a chance to show off its capabilities in terms of fire support in a big way in the 80s and 90s could well solidify a requirement for some kind of large gun battleship replacement. If, say, Desert Storm includes a large scale landing in Kuwait and the Navy is able to do something with the ships in Panama, Grenada or Somalia that is generally accepted as having saved a significant number of American lives I could see the Zumwalt class carrying more and larger guns on a larger and less stealthy hull and being seen more as a solution to the aircraft carrier like crew size of the Iowa class than a next generation destroyer more or less aimed at obsoleting the Burke class.
It might also be possible to come up with a scenario under which the Soviets completed one or two of the Sovetsky Soyuz class ships post war, which would require a POD around '46 or '47 but involving ships not becoming active until the 50s. This would serve no real practical purpose that I can see, but Stalin was apparently very interested in seeing these ships operational, even after the war. With a little ASB intervention (not really ASB I suppose, but much more likely the the navy would have no interest in them and arrange for the ships to be retired ASAP after Stalin's death IMO) the naval infantry might be able to make a case for keeping the ships to ensure strategic parity with the American battleships, eventually resulting in the Kirov class gaining large guns to provide naval gunfire support. Ultimately the biggest flaw here is that there just aren't that many possible Russian amphibious operations, and any kind of large gun ship would be VERY expensive for them.
tl;dr
Not inconceivable to come up with more active battleships more recently than OTL leading to large gun ships with a fire support role, but they are probably more like battlecruisers than monitors in design though not in function. True monitors seems damn near impossible to me.