Any time you measure you use of. For example, a cup of tea, a box of pencils, etc. Say those without “of” and it will sound just as wrong as “a couple books.”

There are a few books I want to read

There are many books I want to read.

There are two books I want to read.

These all say basically the same thing. Take the of out. The reason it sounds so good to this many people is because it has become the norm.

the only time colloquial English would accept the missing “of” is when the phrase is modified to “coupla books” where the “a” is standing for something like “couple o’ books”, just as “twelve o’clock” stands for “twelve of the clock”

There are a couple books I want to read.

Both seem grammatically correct to me. But if I have to reason, I would say the second, because this is my logic.

There are two of books I want to read.

There are two books I want to read.

But can’t you say, “a couple of”? Again, both seem correct.