I mean we can, but it’d be a bit silly. A construction that introduces more confusion than meaning will be naturally dropped or modified.
Or in the case of the OP’s, perhaps never put forth in the first place?
I’m no expert on language change but I wouldn’t expect the OPs proposal to succeed fundamentally because it was put forth and people tend to go go a bit Regina George on that sort of thing (“Stop trying to make fetch happen!”). A better tactic would be to either become a respected and well known writer (or convince one of the superiority of your position) or person of note and begin dropping contraction apostrophes as a matter of a quirky style and hope enough people emulate it to start the ball rolling.
Such as Cormac McCarthy? Because, brilliant as THE ROAD is in terms of plot, mood, character, and theme, his eschewing of apostrophes (and quotation marks) makes the novel worse, not better.
But then, how will we know which it’s or its is meant?
Oh nevermind…
He used apostrophes. It’s the lack of formatting for conversations, so you cant tell if it is narrative or talking or who is doing the talking that is the issue.
I once read a translation of a Russian novel that eschewed all quotation marks. It didn’t say:
“Hello, how are you,” he asked.
It said:
He said hello how are you?
It got to be tedious and I gave up.
I do not have the book in front of me, but I’m certain there are many instances of him writing “I’ll” as “ill”, “we’ll” as “well,” and so forth.
Yes, you can distinguish between these by context. But doing so forces the reader out of the story; you have to stop and go back when you realize that a different word was intended than was perceived. It would be as if someone decided, in speaking, to pronounced the contraction I’ll and the adjective “ill” homophonously.
No, they aren’t equally correct! The word is “cannot”, although I actually had a coworker who claimed there was no such word. “Can not” is good for something like “I can go or I can not go; the choice is mine.” Otherwise, it’s “cannot”.
We have a surplus of “-” ever since “to-day” and “to-morrow” stopped using them, maybe we can get rid of apostrophes and use those extra “-” instead.
Or isn-t that far enough?
An apostrophe is Shift-7 on my keyboard which is certainly cumbersome when typing in English, but I’d never shirk its proper usage, even for convenience’s sake.
Thanks for not spelling it “convience”.
Coming in late: but if I understand the OP rightly, his contention is that apostrophes are unnecessary for word(s)-contractions like can’t, don’t, and similar formations; but he is not calling for abolition of the apostrophe in other roles.
In her Eats, Shoots & Leaves, Lynne Truss (as would be expected, she being a passionate defender of all punctuation), cites a good number of jobs which in her view, the apostrophe rightly and legitimately does – other than for contractions, as discussed in this thread. She lists such uses of it as: for the possessive, in singular / plural nouns; for expressions of time or quantity (e.g. “in one week’s time”); uses involving dates (omission of figures – “the summer of ‘68”, or plural of dates – “the 1980’s"); in some usages, plurals of words (“do’s and dont’s”); and, as mentioned upthread, Irish surnames (O’Neill, etc.). The OP suggests a potential health-related burden from the huge number of, in his view, needless keystrokes for “contraction apostrophes”; however, I would question whether the number of keystrokes needed for that purpose, in fact immensely increases the amount of apostrophe-typing beyond that which is required anyway, for uses which the OP presumably considers justifiable.
Truss – self-confessedly, pro-punctuation to the point of fanaticism – concludes her “apostrophe” chapter with a brief fantasy of the apostrophe being abolished; upon which a “triumphant abolitionist sits down to write, ‘Goodbye to the Apostrophe: we’re not missing you a bit !’ and finds that he can’t.” It would seem clear that certain posters on this thread would take issue with this, asserting that the meaning as above, of “were not missing you”, would be obvious from the context; and that it’s nonsense for Truss to say that the guy, as it were, cant write his sentence without ambiguity.
it shouldn’t be used in titles or names.
There’s no point in doing this until we tackle the much bigger and important project of transitioning to a consistently phonetic alphabet.
Actually when first reading this, my thought is thieves can’t what in you my house. Now this is in the context of apostrophe use so I’m thinking that your single ’ is misplaced. Had I encountered the sentence in another context, I’m not sure how I’d have read it.
If we’re going to semi-retire a character, then why not make it the semicolon? 
Um, you’re welcome? 
The time to stop using apostrophes is when the usage of ‘here is’, ‘that is’, etc drops to near zero. If nobody uses the longer form any more, then the shortened form can probably just be a word in its own right.
Sorry – this misspelling is so very common IRL I almost come to expect it!