“Why is it correct to abbreviate to "brits" and "pakis",
why is it not correct to abbreviate to "alright"?”
The basic thing is this: Brit and Paki are not sound, legitimate words, they are abbreviations and live in the neighbourhood of slang expression. There is a huge difference between colloquial and written language, and one of the basics of education is to teach/learn awareness of such differences.
“Alright” is something else: it is absolutely the product of ignorance, an expression of the user’s lack of knowledge of the correct word. This is seen from the fact that whilst it sounds as if the person is using the correct word, the ignorance is displayed in the writing, the user being utterly unaware of the error.
In a sense, it becomes the same thing as the written confusion between there and their: when someone is speaking, context (pace Keith) makes it clear which word is intended, and hence meaning comes through. However, when someone employs the incorrect one in a written medium, it yells out basic ignorance of English. Which does the writer no good service.
The thing is, it’s so simple to get these things right that refusal to so do seems quite perverse. Why? New rebels without a cause?
There’s a huge conflict between your line that I quoted above and the rest of your post, where you rightly explain the need for, and value of correct use of words. I don’t quite grasp how you can manage, comfortably, to straddle both camps.
Having written my current views on the matter, I have to say that as a teenager I though myself capable of living in two different worlds at once. In school, I would communicate using the best language that I knew, but out of school it was all American teen-slang, with thru rather than through carrying an imagined load of added value. As I aged I realised that was a mistake: incorrect is usually, well, just incorrect.