Your vs you're

[Magick]

Your is the possessive form of you.
You're is the contraction of you are.

"The difference between knowing your shit, and knowing you're shit."
-Unknown

Sadly, most people know and understand the distinction but are too lazy to use the proper one.  They often claim that they're saving keystrokes.  However, the average person types 200 characters per minute and that means they're saving 0.6 seconds per use by omitting the two keystrokes.  This translates to a whopping thirty-six seconds per full hour typing.  Either way, it's not significant and you'll end up waiting that long on a response from the other conversation members.

The other argument is that it's easier on a device such as a phone or tablet.  Ironically, today's devices have predictive text and will often give you both spellings, often with the correct one first.  So this excuse falls flat, too.

[Fool_Hardy]

And finally, I offer the logical argument.

English is stupid.

We teach kids this silly symbol " ' ", called it an ape ass trophy for some reason, and then we said you use it when you want to show possession. Like, that bike is Mike's. (Actual passable sentence that begins with like, I love it.) But then we say wait a minute, we can also use it when we want two words to get it on. Such as, we will becoming We'll. Unfortunately, in mid America, I have heard people read that word aloud as if it were something you could dip water from, they think its a capitol comma so your supposed to drag the word out.

Its quite obvious to most rational thinkers that the ruling class has always had a shallow gene pool. Therefor the edicts and languages forced upon the children of any given nation will undoubtedly eventually become ridiculously ignorant in there nature. They invented the symbol, for the love of Aabahran, they couldn't over 3000 years of written language invent another in order to slow the continued corruption of beautiful minds by ignorant leaders.

[Magick]

Cute.  But entirely irrelevant with one (partial) exception.

And that partial is English isn't stupid.  Horribly complicated, sure.  Even to the point of seeming stupid.  The rules of the language help smooth these over, but it doesn't always work.  So it's "good enough."

Like other punctuation, what's wrong with something having multiple roles?  The period (.), or full stop if you prefer, is used after such abbreviations such as initials and in title contractions.  I'm sure that Mr. Harry S. Truman will agree that we're not actually taking a long pause in the middle of his name twice.
But in the case of contractions and possession, what about it?  You're still using the apostrophe to distinguish between plurals and possessives as well as contractions and full words.  That some people you hear pronounce we'll as well could come down to two things.  The first, is they actually are pronouncing it as we'll and you're just not hearing the inflection change.  That can be difficult at times, I admit.  The other is they actually are pronouncing it well, in which case you can't use one person's dialect or poor speaking abilities to make your argument.
Though how you're using the "capitol comma" analogy with the drawn out out sound, it appears it could be more like it sounds like wheel rather than well.  In which case, that's fine.  Simply because it does sound closer to wheel than well.  But I digress.
I think a topic on this should be had at some point.  Both contractions and possession. Such a discussion should be had there, not here.

Your final paragraph is full of tenuous links, assumptions, wild accusations and complete misunderstandings.  The only thing I'll say to it is that every language evolves over time and is largely dictated by the masses, not those in charge.  The rules of writing are put in place to try to make it easier to convey point between two people without speaking.  And these over time change, too.  As spoken language evolves before written, often is the case that written is in a perpetual state of catch up and is simply doing its best.  In any case, it's easier to invent something like the apostrophe than to rewrite a language.  And you'd need to rewrite nearly every language.  Being said, it'll be easier to invent a new language and form of writing than it is to correct an old one.  They did just that with Esperanto, by the way.

The only thing in your final paragraph, your entire post actually, that's even remotely relevant to the original topic however, is your misuse of there for their.  And I've been planning on such a topic for a while now.