You can't separate armor and protection. Armor is protection. In the atomic age, armor is not viable protection, therefore armor is not the defining feature of modern battleship. The idea of battleship predate armor warship. Battleship is ship of the line, in contrast to cruisers.
(Edit: by the word "separate," I meant to define the terms, not to unlink them in terms of conceptual function)
I'm not separating armour and protection, I'm saying that armour is a
type of protection, along with other types of protection such as hard kill and soft kill protection, active and passive defences.
The entire idea of a battleship is for to to be heavily armed and heavily
armoured -- emphasis on the latter.
There is no such thing as a modern battleship because no ships today are heavily armoured.
Modern capital ships may be heavily layered by all types of protection such as ciws, SAMs, decoys, ECM/EW, but armour is not part of their protection package. therefore they are not battleships.
(Btw a "ship of the line" is a very antiquated term used when sailing ships still formed into lines of battle to deliver and absorb punishment. Battleships aren't be called "ships of the line" -- yes, while they were meant to deliver firepower and absorb it if need be, they didn't form into battle lines against each other)
PS: a ship as heavily armed as a battleship but lacking the armour would be called a battlecruiser. Note how important the battleship's armour is in defining its specific ship type.
I don't think PLAN will seek permanent bases in the Indian Ocean.
Permanent deployment =/= permanent bases. The PLAN currently have a permanent presence in the Indian ocean via their rotations of anti piracy taskforces, without permanent bases I foresee a similar situation in future only with more ships and more capable ships.
Heavy combat assets can be deployed to the theater when Chinese SLOC is threatened.
The whole idea of protecting SLOCs is to do so at peacetime and have the ability to deter aggressive moves against your SLOCs. By the time a Chinese SLOC is threatened, it would already be attacked and cut off, simply on the basis that PLAN bases on the mainland are so far away from the Indian Ocean.
But there is no need to forward deploy them on a permanent basis. It would be counterproductive and raise tension unnecessarily. India, as a fellow developing nation, shouldn't be antagonized unnecessarily. A permanent PLAN base in the Indian Ocean would threaten Indian SLOC as well as India itself. The forward PLAN presence should be ideally accomplished with minimum base support. Foreign base would entangle China into the volatile political environment of the Middle East and Africa. Absalon type warship can be forward deployed for extended period without forward bases. It would make local port calls on a regular basis, receive fuel and stores on a cash-and-carry basis, provide free medical care of local people, provide humanitarian relief when necessary, project soft power on a continuous basis. Accomplish these vital peacetime missions without roughing the feather of the established global naval power or antagonize local powers.
I think your position here can be divided into two parts:
The idea that China shouldn't antagonize India, and the idea that a permanent PLAN presence means permanent bases.
WRT India, the fact is that multiple countries operate heavily in the Indian Ocean. The seas around the Middle East and africa are justifiable interests for many nations around the world to have an interest in defending. So whether India likes it or not, China's naval presence in the Indian Ocean (to be precise, the more western, middle-east/african side of it) will only grow.
WRT permanent PLAN bases -- a permanent PLAN presence in the form of a CVBG or ARG doesn't necessitate a permanent base. Basically, what they would do is perform 3-4 month long patrols with the occasional friendly port visit.
Say, a permanent naval presence in the form of a carrier/LHA/LPD, supported by four DDGs/FFGs, and two or so AORs, can be deployable without need for forward bases. The carrier and AORs staying in theatre for perhaps a few months longer than the destroyers and frigates, the same way as some PLAN AORs have lingered in the gulf of aden longer than destroyers and frigates.
Current PLAN taskforces to Aden are not deployed from forward bases -- they operate in the same way as you've suggested an absalon type warship should. They are supported by AORs, make local port calls, and do flag showing visits with local regional states.
I'm suggesting the PLAN will seek to do the same in future, only expand that by deploying more ships and larger ships for the same role, and they won't need permanent bases either.