Why is a castle called a rook?

If I understand your "reasoning", rooks changed from chariots to towers and presumably bishops changed from elephants to the abstract shapes they now have because it was easier to carve the newer pieces. Knights remained horse's heads because horses still had a military function. This fails to explain why new more-military shapes weren't created for other pieces, or knights modernized.

You claim that the simplification had to do with easier carving for inexpensive sets. Yet the changes in rooks and bishops came about long before the industrial revolution and invention of plastic that you say were responsible for cheap sets. Why then did expensive sets not retain the ornate carved shapes? Where are all the cheap pre-industrial, pre-plastic sets with simpler knights?

Again, if your thesis that pre-industrial age well-to-do chess players wanted beauty in their pieces there was no sense to changing the shapes of all other pieces than the knight. If your idea that chess players wanted their pieces' shapes to have some relation to war is correct, the shapes today's pieces would reflect things used in Renaissance warfare. If the pieces had to be simplified to reduce costs, the knight would also have changed.

Finally, how does any of this answer the original question of why English speakers came up with the name "rook"?

That was the term Carl Jaenisch used for the king’s knight, but the queen’s knight was a mare. See https://www.chess.com/article/view/notation-1

Cracker Jack refers, of course, to that popcorny snack food.
There is no evidence that it's related to the playing card.

Middle school etymology does not address the question posed by the OP

The Oxford English Dictionary's oldest definition of "rookie" is "A new recruit, especially in the army or police force", first documented use from 1868, before professional baseball existed. The oldest reference to the use of the term from sports was in 1902.

Yes, the English word "recruit" comes from the French "recrue", borrowed in the 17th century. The English word rookie is a 19th century creation with no French equivalent.

Idiocy. The Russian word for 3 is (transliterated) "tri"--pronounced tree. Does this mean that those large plants outside your home got their English name from that Russian word?

Yes, but that doesn't mean that the old Russian word is the source of other newer words that sound like it.

I think you will be able to spot one in the nearest mirror.

Just judging by the pointlessness of some people's posts.

I can't think of anything that would properly express my estimation of what you have "taught" us and still remain within the bounds of civility.

Good to see the mods beginning to clean up some nonsense. Perhaps they'll also lock this thread, which has gone completely off the rails in the past couple of days.

Some members have been muted for using language that is in every movie every made and been warned for using words found in the history of science by quoting academic websites. At least you are safe from censure for quoting actual science.

You should read 1984 instead of referencing it the manner of conservative politicians who reverse the text, just as they manufacture quotes because George Washington never said what they wanted him to say.

Wikipedia says that 'rukh' means 'chariot' in Persian language. It makes sense, rook moves straight like a charging chariot.

In Persian, we call the rook "rokh" or "ghalleh" (which means fortress). I'm not a linguist so I don't know the relation of rokh to a chariot.

That's actually very funny to visualize

You mean, Why is a "Castle shaped thing, or Castley looking thing, called a Rook(??)