personal opinion, dump it.
but then again I am all for getting rid of 99% of the nonsense that is formal english. thinks like using an ’ in an abbreviated word…what the Frak is that all about? you leave out a letter to save space/time and REPLACE IT WITH SOMETHING ELSE THAT TAKES SPACE AND TIME AAAAAAAAAAAAA!!!
IIRC, something like 93% of all communication is non-verbal. When reading the written word, this makes precision that much more critical in order to impart accurate meaning, since the audience is missing the non-verbal cues which might illustrate what exactly is intended by the words. I feel that the apostrophe in possessives helps to achieve this goal, by clearly illustrating that “this word is a possessive.” The willy-nilly manner that other people misuse the apostrophe simply speaks to ignorance of its proper usage and not to a flaw in the usage itself.
If a person is writing with the intention of being understood, it logically follows that they will make some effort to obey the rules as they are prescribed. Unfortunately, that is a bit of a moving target with regards to some of the finer points, but the sentiment holds true, IMO.
Written language is a fairly new innovation in the grand scheme of things, and we are still seeing many of the associated growing pains. I don’t think that means we need to start throwing babies out with the bath water, however.
You don’t actually use contractions in formal writing, because (as you point out) they’re mostly spoken shortcuts. You write out the full “do not,” “they are,” “is not” and so on.