Problem with these two class of ship are that they cost a lot of money for build, a lot of money for keep them operational... and when they are in maintenance cycle, it take years...
Clearly you missed the very first line of my post when I said: "It's more due to cost of constantly keeping large ships in service in peace time." That, of course, is in reference to all large ships, not just certain ones. 
Also the largest problem in trying to use the Russian Navy as an example of cost and maintenance cycles, was their obvious social and economic collapse of the soviet union. Pretty tough to maintain a powerful warship when you have no money and a third of your country is giving you the middle finger and creating their own countries. Look at the US. We maintained battleships into the 90's. Just as before, even though those ships are not in service, we can bring them right back in because they are still somewhat maintained.
Well, they are called battlecruiser now but they are similar in size to battleship and have more firepower... for example :
I'm well aware of the battlecruiser class created by the Brits when they ditched armor for speed, while they may be similar in size, their firepower isn't nearly on par with a battleship, and their displacement is around half. Kilrov 28,000 tons fully loaded. Iowa (Though designed in the late 1930's just prior to WW2, used as a comparison because it was the only class of battleship in service in the 1980's by a navy that could rival the Russians) 58,000 tons fully loaded. Amusingly enough, even an Iowa that is considered to be light at 45,000 tons of displacement still has a top speed of 3 knots faster then the Kilrov. So the sacrifice in armor for speed seems to be for nothing if a ship designed almost 40 years prior not only has more armor, but still can go faster... But in reality, size doesn't really mean much to warships because Cruisers, for which the Kilrov really is, can be similar in size to WW1 battleships, but destroyers, such as the newest classes, can be even larger then that, which puts them as similar in size, or even bigger then WW1 battleships, yet we still call them destroyers none the less.
Now to firepower. Kilrov: Their biggest gun is their twin 130mm... Basically a 5 inch gun. The Iowa? Nine 16 inch and twelve 5 inch guns. Total guns: Kilrov: 15. Iowa: 21. Offensive Missiles: Kilrov (Ushakov only): 34, (the other three only have 20). Iowa: 48. Defenses: Kilrov: 332 Surface to air missiles. Iowa: four 20mm Gatling cannons that can spit out 4500 rounds in under a minute and send them more then 2 miles down range. I'm willing to give that one to the Kilrov based on the fact I like missiles better then bullets, but then again, you've only got 332 chances to hit your target who in all likelihood can make your missiles miss with flares and chaff, and you can't really use those to defend against incoming missiles. The phalanx on the other hand, will hit whatever its aimed at because you can't force it to miss, and its an automatic system which means the only input from us is reloading the ammo compartments and allowing it to shoot in the first place (which in all honesty is only human controlled because of friendly fire concerns).
Let's just face the facts here, the slight retrofitting of the 30 something, damn near 40 year old Iowa class Battleships around the same time as the designing and building of the first Kilrov, put the Kilrov to shame. The Kilrov is slower, much less armored, and severely underwhelming in the weapons department. The only advantage the Kilrov has is its nuclear powered engines which gives them an approximate 30 year lifespan between refueling (but not resupplying which makes this a moot point) should they want to maintain a 20 knot top speed for that entire lifespan which means the Iowa would be going nearly twice as fast as it. The armored cruiser/battlecruiser just doesn't have what a true battleship can bring to the fight.
Just be glad the US never built any of the Montana Class Battleships or the weapon systems would be much further in favor of the true battleship. Twelve 16 inch cannons, twenty 5 inch guns, for a total of 32 big guns, forty 40mm AA, fifty six 20mm AA, totaling at 96 defensive guns, and this is just for WW2, this ship would have gotten all of the retrofits over the years that the Iowa class got instead, so this beast would be loaded with missiles and the four Phalanx Gatlings instead of all of those AA guns during the 1980's.
As for a mix of battleship and carrier, we have it already on earth
Holy crap, not even close. Two 100mm (4 inch) guns 10 torpedo tubes and 12 ship to ship missiles isn't even in the same ballpark as a battleship, let alone a cruiser, let alone a destroyer... Its a light aircraft carrier with meager non aircraft offensive capabilities. That carrier only carries 30 aircraft... The Nimitz class, designed and built around the same time as the Kiev class, carries 90 aircraft. Granted the Nimitz doesn't carry anything even worth mentioning as a non aircraft offensive weapon, but when you carry 3 times the aircraft, are a couple of 4 inch guns really worth worrying about finding a spot for? So no, we do not have a melding of battleships and aircraft carriers today. When one carries at least a pair of main guns ripped off from an Iowa class, them big old triple side by side 16 inch barreled bad asses and has them slapped onto either end of the flight deck, carries 8 times as many of those little 4 inch guns, and houses a few dozen ship to ship missiles (not including anything on the defensive side of things like sea sparrows or phalanxes) then go ahead and make your claim to them already existing. But today? HAH! No. By that comparison, I could claim that battleships in WW2 were battleship and aircraft carriers combined because they could maintain and launch two to four seaplanes. Granted these seaplanes were used as scouts and not actual bombers or anything, but if you think a single twin 4 inch gun is the same as nine 16 inch guns, then I guess the seaplanes were great bombers that changed the outcome of the war.
So in other words, a Battlestar right?
I've never had the time to watch the new series so I don't know how things go in that, but the old series, even though they had main guns that they treated like the main guns on a battleship, as far as I remember, they were only really ever used with the point defense guns to ward off incoming threats making these guns just larger defensive weapons, not offensive guns. They still used the Vipers to take down large enemy ships. So in this instance, no. If in the new series, they use them like a battleship would to shell structures and other ships as an actual attack option, then yes, I could see that being a good example. The problem in sci-fi is, no one is really willing to combine the two ships because they think like modern day navies. Carriers are for wings of strike craft, battleships (if they even include them) are loaded up with big hulking guns that make everything else look like toys, and frigates are sprinkled in for a variety of purposes. In space, you don't need the flight deck, so load that bitch up with the biggest most powerful things you've got. Just take a battleship, forget about everything that is duplicated between both ships, add in an area to store your strike craft, add in a couple launchers on one end of it and receivers on the other, and bam, you have a battleship/aircraft carrier.
I guess the best example I can think of would be the Eclipse Class Super Star Destroyer from Star Wars. It was designed and built to combat and destroy other large ships, destroy space stations, and even blast a good chunk out of a planet should they choose to do so using a superweapon like the deathstar, which was also used to one shot kill other capital ships. It was armed with thousands of other offensive weapons and carried nearly 700 strike craft. That to me is a battleship melded with an aircraft carrier. It was armed to kill everything it encountered, it carried a crap ton of strike craft that could do the same thing.
