I would say that yes, there are contexts where only "all right" is acceptable. As an example: Are any of the answers wrong? No, they are all right i.e., all of them are correct.
I have found that alright seems to be following the example of all ready vs. already and all together vs. altogether. In both cases, as I did above, one could add the phrase "of them are" to each of the former terms and make it completely clear what is meant, whereas each of the latter terms have entirely different meanings.
Alright has come to mean acceptable, okay, and safe, as in "the kids are alright" - very much a comforting phrase if there has been some kind of accident or the like! "The kids are all right" in that same context would have an extremely confusing connotation: the kids would not all be correct after an accident.
I would also like to point out that the way a word or phrase achieves acceptance and legitimacy is by usage, and "alright" certainly has this on its side!