As far as I know, I think "见字如面” literally means when you see someone's letter, it's as if you were seeing him or her face to face. So I believe this word sort of indicates your familiarity with the letter guy and how glad you are when you receive his or her letter.
From museum archives, we can see this phrase appears in lots of letters among family members, i.e., husband and wife. At least in these examples, writers and the receivers know well each other and have already seen handwriting before. So it definitely indicates closeness and has a fairly strong emotion.
In other words, it's NOT just politeness of a simple greeting, such as 'Yours', 'Regards' in English. It's weird if the letter is to a stranger.
Strictly speaking, this expression can only be used in the same generations. So you can use it if you write a letter to your sisters/brothers but not to your parents. In a preparation document for the college entrance exam, there is an example use of this phrase. Here is a link! It points out that it's incorrect if you use it to write a letter to your grandpa.
That said, the use of the phrase is pretty flexible nowadays. I see people use it in an email as a simple greeting. Given the fact that the phrase now is not commonly used, especially in handwriting letters, I think it's fine with both opinions.
Your understanding is partially correct. This phrase is used at the beginning of the letter to address the receiver.
The meaning of the phrase - "see the letter as we've met", or "see the letter as seeing me/each other", indicates the closeness/close relationships between the letter writer and the receiver, but does not necessarily have emotion attached (as a greeting).
If I didn't make mistake, the original phrase should be "见字/信如晤(meet)” then.
見字如面 sounds similar to 見字如見人
People can tell who you are by your handwriting.
A person's handwriting is like his face, it is recognizable and it leaves an impression
I don't believe it is a greeting. The one who read a letter from a friend might feel he is looking at his friend's face in the handwriting, but that's a reaction to the letter, the one who wrote the letter wouldn't presume it