Trump floated this idea in 2015, and military historians shot him down pretty quickly.
thickness of armor is immaterial against a torpedo that detonates under the keel, and modern supersonic missiles can penetrate battleship armor. So making huge thick armor doesnt protect you.
and 16" guns have a range of about 25 miles, while cruise missiles that can sink a battleship can travel hundreds, even thousands of miles.
So, first day of battle, your $10 Billion dollar Battleship sinks after being hit by a couple of $1 million dollar cruise missiles.
The only way we could ever pay for a fleet of those is to cut the taxes of Apple and Facebook, then the huge increase in prosperity would allow us to build 20 of em...
The military is actually working on long range munitions projects. They currently are wanting to deploy a long range 155mm with a range of 75mi.
The goal is to increase range and be able to deliver the same effect at distance as the current non-nuclear cruise missiles.
I suspect that they are only a couple of years away as they are starting to get quotes on the equipment to manufacture the new artillery. Much of this is being designed to be retrofitted onto the existing under-carriages of existing artillery to reduce the costs and speed deployment.
As far as if a battleship would be practical in this day and age, I think you need to change your assumptions of what a new battleship would look like. It is not necessary to use the armor plating to protect the ship as there are better and cheaper technologies today that will give superior results.
Having large 16in. or larger barrels is not necessarily the only way to deliver the desired payload and destructive force.
A lot of this might sound like pie in the sky, but I seriously do see the possibilities of relatively cheap, low tech munitions delivered at an extended distance being very practical.
A cruise missile technology has many advantages when used against a specific target. The downside is cost per unit and the limited number that can be available in a given time window. In essence a prolonged attack by an enemy will overwhelm a cruise missile weapons system if enough low value targets are presented. The slow bleed scenario that is often used by inferior forces.
In comparison if you can deliver a low cost munition at a long range with a rapid delivery for an extended period of time, you could feasibly control a battlefield for a long duration without stretching the available resources.
This gets back to the problems of our current Mideast situation in that we are encountering hostile forces with relatively low technology that are able to take out high-tech aircraft.
Sometimes being able to throw rocks at the enemy is the best solution.
Now the big question is if the military can keep technology creep out of this.