To begin here is the relevant passage from Ayn Rand's Fountainhead

"But, I don't understand. Why do you want me to think that this is great architecture?" He pointed to a picture of the Parthenon. "That," said the Dean, "is the Parthenon."

"So it is."

"I haven't the time to waste on silly questions."

"All right, then." Roark got up, he took a long ruler from the desk, he walked to the picture. "Shall I tell you what's wrong about it?"

"It's the Parthenon!" said the Dean.

"Yes, G*d damn it, the Parthenon!"

The ruler struck the glass over the picture.

"Look," said Roark. "The famous flutings on the famous columns---what are they there for? To hide the joints in wood--when columns were made of wood, only these aren't, they're marble. The triglyphs, what are they? Wood. Wooden beams, the way they had to be laid when people began to build wooden shacks. Your Greeks took marble and they made copies of their wooden structures out of it, because others had done it that way. Then your masters of the Renaissance came along and made copies in plaster of copies in marble of copies in wood. Now here we are making copies in steel and concrete of copies in plaster of copies in marble of copies in wood. Why?"

End quote

It has some truth to it. The origin of the fluting is very much debated. The fluting was definitely in wooden columns before stone columns but why it was done in the first place and why it was carried on isn't clear.
It is possible the fluting was originally made as logs were shaped using an adze. A curved adze doesn't stick nearly as much as a flat adze so the fluting may have resulted from simply carrying a pattern naturally made by the tool evenly around the log column.

Many trees naturally have a kind of fluting if you look at their shape with the bark on. This may have inspired ancient architects to copy it to make the columns appear more natural. There are no such trees native to Greece or the surrounding region so I find this one unlikely.

The fluting may have been done to create a plastic look to the buildings. Columns made from natural material wood/marble will each have slight variations. By carving a common pattern on each column the appearance of the variations are minimized. The fluting may have been merely an effort to make the building appear as a single solid figure.

As for the triglyphs they similarly appear in wood before marble. In both instances they serve a similar purpose first they raise the roof. Second they frame and hold the panes of the metope. Finding a single gigantic slab of material perfect for the face of the building is difficult. By breaking it into smaller sections you can create elaborate works with greater ease. Each section can be carved on the ground and then lifted into place multiple masters can work on each sculpture etc.

But the Greeks didn't invent columns. The Egyptians actually used columns before the Greeks. Egyptian columns often had convex rather than concave fluting. This made Egyptian columns look almost like a bundle of reeds. A picture showing different columns

Warning the following paragraph has my personal opinion on Ayn Rand some people may be angered, bemused, unaffected or driven to long bouts of depression by its contents. Reader discretion is advised.

As with many other parts of Ayn Rand's works the subject is much simplified in order to be ridiculed. There are many reasons for the fluting and the triglyphs some of which may be as simple as copying the aesthetics of previous buildings. However, the suggestion that functional features of aesthetics do not carry over between materials is ridiculous. Ayn Rand reduced beauty in architecture into a typical simplistic black vs white mentality which I feel is a common theme in her works.

I'm done ranting the references below are safe for all readers.

Great website for a quick introduction to Greek columns and the Parthenon

For those interested in studying further check out

Greek Architecture by Arnold Walter Lawrence