The consternation around the usage of “on-premise” is understandable. For those in IT, it is a benefit to be as precise as possible. It makes communications efficient and eliminates wasteful ambiguity. “On-premise” often feels forced into usage my marketing folks who couldn’t be bothered to add an extra letter for the sake of clarity.
Now, I have argued that language is essentially an arbitrary series of signs anyway. This is essentially a functionalist argument that language exists to be understood, so if we understand what is meant when we say “on-premise”, then it is an acceptable usage.
Merriam-Webster recently posted about the origins of the term “premises” that shows the word meaning IT folks so adamantly defend was created by just such an accepted understanding. The word came from the legal usage of the word “premise”, referring to prior parts of a contact that dealt with property specifics. Over time, this became accepted short hand for the property itself.
As far as modern usage of premise vs premises, I think the whole thing could be solved by simply moving to “on-site” as the preferred parlance of IT. Of course, it would only be a matter of time before we see “on-sight” coming to a slide deck.
In real estate deeds, the premises are the first part of the contract, where, along with the names of the grantor and grantee, the specifications of the property—encompassing building, lands, and tenements—are described in detail. Since many of the later clauses of the contract need to refer to the first part and its descriptions, the word premises came to identify with the property described.