Interesting. "Alright" is listed in my ancient Chambers Twentieth Century Dictionary as "an unaccepted spelling of all right". That was in 1972, so this naughty contraction had clearly wormed its way into sufficiently common usage at least since the 1960s (hmm, Wiki style guide says no apostrophe here, but is that definitive?) and is still, apparently, in common usage more than 40 years later.
You're correct that "alright will eventually establish itself in the long run" because if enough people use it then it will become "correct". The fact is this is how English (syntax and words) has evolved to become what we know today. Purists and strict grammarians may resist change as an abomination, and many of us "fight" against "incorrect" usage, but change is a good thing. One of the reasons English has become so dominant is its (yay, no apostrophe!) uncontrolled ability to evolve new words, new constructions, and new usages. Change is the strength of the English language, keeping it fresh, vibrant and powerful. Contrast the pitiful attempts of the Académie Française to regulate and control the French language and consider the current status of French as a World language.
All right, personally I don't necessarily agree with many of these changes but, to use the Vogons' favourite phrase, I am afraid "resistance is useless"