IDK
Why is a castle called a rook?
Stop all this arguing and listen to me. Take a deep breath, close your eyes and say "castle" 5 times followed by saying "rook" 5 times. After doing this for 12 hours straight, take 3 shots of whisky and go to bed. You will wake up refreshed and not worry about such crap.

Isn't there a term for someone who has long conversations with themselves?
Yes, some one who doesn't want to talk with stupid people.
Dude. You are sitting on a park bench rattling on about nothing. People walking by see you talking to yourself. Occasionally, someone else will say something as they are walking by.

Answer this simple question.
What is the rook in the original Indian war game? What is it?
No one knows. The earliest written reference to chaturanga dates to the 7th century (the poet Banabhatta's "Harshcharita") but makes no mention of the pieces. The oldest existing "chess" set is the Afrasiab set, found near Samarkand and probably dating from the early 8th century. There is a chariot in this set, but there is no way of knowing how things might have changed as the game spread from India to central Asia.
The "four arms" (from which the name chaturanga devolves) of the Indian armies mentioned in the ancient Mahabharata (at least as old as 400 BC) do contain chariots, but by the time chaturanga was invented the chariot had fallen into disuse in Indian warfare.
In any event, nothing from ancient Indian history explains the actual question of how the name "rook" became the English-language term for the piece, or why it is shaped as a tower.

Answer this simple question.
What is the rook in the original Indian war game? What is it?
There is a chariot in this set, but there is no way of knowing how things might have changed as the game spread from India to central Asia.
It is still a chariot in Chinese chess. Still a glyph of a chariot.
車
And it is a stone tower and called "tour" in French, "torre" in Italian and Spanish, "turm" in German, all meaning tower. What does any of this have to do with the original Indian name?

Of course all the oldest "chess" pieces ae stone carvings (wood doesn't last as long) so your explanation makes no sense.

If easier carving were the motivator in the shape of modern chess pieces, why is the knight still a horse's head? Also, is the Chinese chess equivalent of the bishop inscribed with the glyph for an elephant?

Answer this simple question.
What is the rook in the original Indian war game? What is it?
There is a chariot in this set, but there is no way of knowing how things might have changed as the game spread from India to central Asia.
It is still a chariot in Chinese chess. Still a glyph of a chariot.
車
And it is a stone tower and called "tour" in French, "torre" in Italian and Spanish, "turm" in German, all meaning tower. What does any of this have to do with the original Indian name?
Nothing

If easier carving were the motivator in the shape of modern chess pieces, why is the knight still a horse's head?
Good question.
It is to distinguish the expensive sets from the cheaper ones.
I can easily poke a circle with a Bic pen to make eyes on a horse's head.
But the realistic ones are where you can justify the extra costs. $$$.
"If it don't make dollars, it don't make sense." - Jim Cornette
But even the cheap chess sets have knights shaped like horse's heads.

But when round towers became the shape of the rook, plastic hadn't been invented yet--that explanation makes no sense.

Your explanation for the shape of the modern rook is that it was easier to carve from a wooden cylinder. This would mean that the knight should also have changed into something easier to carve, but it didn't. All this happened centuries before the invention of plastic, so your mention of that is totally irrelevant.

But when round towers became the shape of the rook, plastic hadn't been invented yet--that explanation makes no sense.
The "ring tone" you hear on your cell phone is a recording of a real telephone striking a real bell making real sounds, like a musical instrument in a telephone.
So if you were to use an analog telephone, yes, it would make the same "ring tone".
But that ring tone is real. Your cell phone ring tone is fake. It is a recording of a real ring tone.
Slow yourself down and think.
Considering how quickly you come up with meaningless "answers" to simple questions, perhaps you should listen to your own advice. Again, plastic has no relevance to the shape of the rook or knight.

But when round towers became the shape of the rook, plastic hadn't been invented yet--that explanation makes no sense.
The "ring tone" you hear on your cell phone is a recording of a real telephone striking a real bell making real sounds, like a musical instrument in a telephone.
So if you were to use an analog telephone, yes, it would make the same "ring tone".
But that ring tone is real. Your cell phone ring tone is fake. It is a recording of a real ring tone.
Slow yourself down and think.
Considering how quickly you come up with meaningless "answers" to simple questions, perhaps you should listen to your own advice. Again, plastic has no relevance to the shape of the rook or knight.
Brandolini's law.

Harold Staunton came up with his chess set design in 1849. The first variety of plastic (parkesine) was patented in 1862, and easy-to-manufacture plastics that be molded into any shape are a 20th century development. You are truly traveling through the Twilight Zone if you think plastic was the reason knights are shaped like horse's heads. There were plenty of cheap chess sets in existence before the invention of plastic.

@mpaetz
As I said, realistic wooden horses are in expensive sets.
Did you know that Computerized Numerical Control Routers also did not exist in 1849? Cheap chess sets with carved horse's heads for knights existed for centuries before it became even easier to make them with plastic. Still not any reason to think the shape of all chess pieces has to do with easy carving.

There were plenty of cheap chess sets in existence before the invention of plastic.
Do they have realistic horses?
Yes.

Harold Staunton came up with his chess set design in 1849. The first variety of plastic (parkesine) was patented in 1862, and easy-to-manufacture plastics that be molded into any shape are a 20th century development. You are truly traveling through the Twilight Zone if you think plastic was the reason knights are shaped like horse's heads. There were plenty of cheap chess sets in existence before the invention of plastic.
Nathaniel Cooke came up with the design. Staunton endorsed it, a move that was vital to its commercial success.
IDK