No need for any UKSK and S-500s
You don't want to put all your eggs in one basket.
You want to spread them out as much as possible.
You are contradicting yourself... first you say you don't need the carrier to carry eggs and then you say you don't want all your eggs in just one type of ship... you want every ship to carry some eggs.
Your latter point is of course the one they seem to be going with... instead of heavy anti ship missiles in a couple of big vessels like Kirov, Slava, and Oscar, every ship from corvette to carrier and also pretty much every sub that is not an SSBN will carry land attack, anti ship, and anti sub missiles in their standardised UKSK universal launchers... they are called universal because they will carry all new anti ship and land attack and anti sub missiles, but also because all vessels big enough to carry them will have them.
this means instead of specialised ships with specific missile loads... the Udaloy could be a multi role vessel but is equipped with subsonic anti sub missiles with a secondary anti ship role... Sovremmeny has anti ship missiles in the form of the Sunburn... the new Frigates will have twice the fire power of these destroyers and the new destroyers will have four times the fire power... the Udaloy having 8 anti sub missiles and the Sovremmeny having 8 anti ship missiles the new destroyers will have 4 UKSK launchers each with 8 tubes... so one new frigate can carry 16 anti ship missiles and 16 anti sub missiles... so the fire power of two Udaloys and two Sovremmenys... or more importantly it could carry the same firepower as one of each vessel and have 16 land attack missiles... with a range of 5,000km... which is comparable to the firepower of old SSBNs and something no Soviet surface vessel could manage.
A UKSK launcher takes up little space and could be placed almost anywhere on the new carriers... they certainly wont have dozens of launchers, but just for anti sub protection they will almost certainly have at least two... I mean if they can fit two to a corvette then they can fit two to a carrier.
In terms of the S-500, it will protect the carrier from all sorts of long range ballistic hypersonic threats... the whole point of a carrier is to extend vision and reach so it will have AWACS and it will have very large sensor arrays that smaller vessels wont be able to accommodate. the Carrier will also form the centre of the battle group... coordinating operations in defence and attack... it will certainly have naval S-400 and likely S-350 and 9M100 for self defence, and so why would the vessel most able to see long range threats not be given a weapon to deal with them? S-500 on the carrier as well as on the cruisers means more missiles available and better defence of the carriers and cruisers... which is something they need.
I would expect PAKET-EM would also be carried to defend against hostile subs and incoming torpedoes.
With its huge air wing, the carrier will already be the most expensive asset in the fleet. If you add more capabilities it would be at the expense of space for fixed and rotary wing aircraft; and will increase the cost and complexity.
It is always going to be expensive... if we translate this to the ground forces are you saying that the major air fields of the Air Force should not have S-500 because it makes them more expensive and restricts some airspace above the launchers for use by aircraft...
Carriers are going to be expensive... so why would you not protect it with your most capable long range SAM?
Just have it for the aircraft, with some point-defence Pantsir systems and maybe some naval Tors.
You mean the American approach?
The Russian Army does not rely on the Russian Air Force for air protection, and I don't think the Russian Navy will rely on the aviation component for air defence alone either. there are lots of places on a modern carrier where you can put vertical launch missiles that wont effect the capacity to carry aircraft...
No need to give the U.S. a reason to start investing in actual anti-ship missiles instead the joke of LRASM shall suffice for them.
More importantly there are some sea states and weather conditions where aircraft simply can't operate... but missiles can be launched by both sides...
the aircraft form another layer of defence and another layer of extended sight, but that is no reason to remove inner rings of protection... Frigates and Corvettes wont have the sensor range to effectively use S-500 so if you want it at sea operating effectively you need every big ship able to carry it to have it. Just as the cruise missile capability is not credible when only a few attack nuke subs have them like in the 1980s. A modern Russian fleet where every vessel can be carrying some makes the cruise missile threat rather enormous for every member of NATO including the US and Canada.