grammaticality - Is it correct that "etc." can not be used together in a sentence with "for example" and "such as"?

I just read an article from a Chinese website for English teaching which mentions that point. For instance, one can't say:

"I can play quite a few musical instruments, for example, the flute, the guitar, the piano, etc.".

The correct one should be:

"I can play quite a few musical instruments, for example, the flute, the guitar, and the piano."

Is it possible to find any references to prove that?

Answer

Apart from being redundant, as Mitch said in the comment, I don't think etc. fits very well in that example. There is a nuance to the use of etc. that Wikipedia sums up:

The phrase et cetera is often used to denote the logical continuation of some sort of series of descriptions

"Logical continuation" is the key here. Consider these two sentences:

A balanced diet should include fruits: apples, oranges, etc.

The fruit basket contained some of Bob's favorite fruits, for example, apples, oranges, etc.

In the first example, you can logically continue the list of examples by substituting any type of fruit. But in the second, you can't. You have no way to know what other types of fruits Bob likes to eat, nor what was in the fruit basket.

I don't think it's necessarily wrong to use it in that way, but it does feel very awkward to me.