Why is there no plural 's' after "hundred" or "thousand" in cardinal numbers?

Hundred, thousand etc. are used as adjectives. So, they are not changed to plural number by adding -s to them. For example, Twelve thousand rupees. Here, Twelve, thousand -- both are adjectives qualifying the noun rupees (indian currency). Three hundred apples, etc. Similarly, in "Two dozen eggs", dozen is used as an adjective. Hope, it is now as clear as daylight.

One might explain the singular of "thousand" and "hundred" as in 5,400 in this way: five standing for a unit of one thousand and four standing for a unit of one hundred.

There is not necessarily a logical grammatical justification. In the case of million, usage patterns have shifted.

"Two millions" vs. "Two million"

According to Google Ngram, "two millions" was long the standard expression. However, starting around 1850, its usage declined while "two million" rose in popularity. Around 1920, "two million" became the new norm, and today "two millions" is rarely used.

"Two thousands", "Two hundreds"

In contrast, neither "two thousands" nor "two hundreds" has ever been accepted usage.

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If I had to speculate on the reason for the difference, it is probably because million has Latin origins, whereas hundred and thousand have Germanic origins. Therefore, the Old English-based inflection rules have always applied to hundred and thousand, but the French-based rules for million have only recently started giving way.

In English words are pluralized only if they are used as nouns, so if we pluralize a number, we treat it like a noun:

My telephone number contains three fours.

Thus if you say:

twelve thousands, three hundreds, and forty-five apples

this would mean you have only 45 apples, and that you also have 12 thousands, and 3 hundreds. Of course, this wouldn't make sense, because how can you "have" a number like a thousand?

So, if we are using a number as a quantifier, not as a noun, we don't pluralize it.

Another way to look at this is by building up the phrase from smaller parts. First, let's multiply the number of things we have. Compare:

an [apple] (singular)

twelve [apples] (plural)

with

a [thousand apples] (already plural)

twelve [thousand apples] (still plural)

Next, let's add numbers of things we have. Compare:

red apples, green apples, and yellow apples

red, green, and yellow apples

with

twelve thousand apples, three hundred apples, and forty-five apples

twelve thousand, three hundred, and forty-five apples