Yet even in informal use, smart writers avoid using the hyphenated variant all-right. Hyphenation adds nothing substantial here. Often a hyphen will indicate that multiple words in a phrase are connected in meaning as a modifier for another word, particularly a noun. But that’s not needed in this case, since everyone understands that all and right work together in all right. Smart writers avoid unnecessary constructions just as they would avoid unnecessary words.
However, it’s more difficult to make a case for excluding alright. English contains some instances of related words with different meanings, already and all ready, for instance. Because all right and alright have no distinct difference in meaning, some grammarians believe that alright should never be used, thus supporting only one word for the one meaning.
That argument ignores the acceptance of cannot and can not in the language. Both of these terms have the same meaning, and the use of either one is just as acceptable as the other. It’s simply a matter of stylistic preference in the writer. I see all right and alright in the same light. For me, either expression is all right (or alright, if you prefer).
But that discussion becomes moot when considering formal audiences like those for technical writing. In that instance neither all right nor alright is appropriate. Effective writers will select a more formal word like acceptable.
All-right is never all right, but alright may be. Effective writers of any text consider their audience. When that audience is more formal, as is common in business and technical settings, the words used should convey that sense of formality. That makes for a better presentation of content, and that conveys a better image of you, your brand, and your organization.