That doesn’t sound right… but why not? Plenty of other contractions sound perfectly fine at the end of sentences.
This site explains that there are “weak” and “strong” versions of some words, but those distinctions exist only to our ears and not really by rules of grammar. It argues that, for whatever reason, English speakers don’t end sentences with “weak” forms.
It sounds wrong to a native speaker, and would never be used naturally by one. That’s exactly what “grammatically incorrect” means. So apparently there is some grammatical law that prohibits it, which may or may not have been discovered and named by some linguist.
That depends on what you mean by grammatical. If you’re using a linguistic definition, than no, it’s not grammatically correct, because a native speaker would reject a formulation such as “I’m smarter than you’re.” as being wrong.
AFAIK, there’s no grammatical rule which prohibits ending a sentence with a contraction. It does sound very awkward, so most of the time, it’s best if you don’t.
It’s wrong because that’s not how English works. It’s no different than if the student had written “the ball red” or even “the red, big ball”. There’s nothing objectively wrong with such formulations except that they’re not how generations of speakers have chosen to organize the language.
Usages differ in various parts of the English speaking world, with respect to which vowels can be left out and when:
America; It’s a pity.
Ireland: 'Tis a pity.
A contraction reduces a spoken expression to its phonetic. “Can’t” is pronounced with one syllable, “cannot” with two. If you don’t want to show that is to be pronounced that way, you can’t use the contraction when you write it.
The cadence is wrong. Cadence is an important part of language, even though it isn’t part of grammar. You can make up words, and as long as they follow the morphological rules for words in English (“duggish” could be an English would “pfeeoar” could not); you can then come up with sentences that either do or do not use English cadence, and ask native speakers which sentences sound right, and which do not, and you will get very high levels of agreement.
English sentences need a stress at the end. That’s why iambic pentameter sounds so natural that people barely notice it’s metered, but Poe’s “Once upon a midnight dreary,” makes you feel a little uneasy.
Contractions like “you’re” and “you’ll” are dismissive of the verb as semantically redundant while accommodating its grammatical necessity, as in “you’re a fine fellow”. But in a sentence like “You may think you’re not opinionated, but everyone tells me that you are”, the “are” at the end carries the stress and the core of the meaning. It’s a completely different usage.