Why do some abbreviations not use periods?

I was going to ask “not require” periods, but I think (at least according to MS Word’s spellchecker) that its not even optional in cases like:

CEO

and

COO

and, I think, the PO

in Post Office Box.

Why the heck not?
and what are some others?

Generally, according to most modern style guides, abbreviations only use periods when they might be confused with an actual word (in. for inch, for instance). Most others do not. According to The Chicago Manual of Style:

This is from the 13th Edition, but I think the newer one would agree.

Of course, it’s all on a case-by-case basis, ultimately.

The master speaks.

Heh. I should probably read the entire OP before I respond to things.
Usually, you don’t use periods with acronyms, such as what you’ve described.