The boring answer is: The phrase "regular grammar" means what it means, because we have decided that it means that. Had we decided it should mean something else, it would mean something else.
That aside, it is of course legitimate to ask whether
Definition A: "A regular grammar is a grammar that is either right-linear or
left-linear."
is a better definition than
Definition B: "A regular grammar is a grammar that describes a regular language
(which we've already defined, eg via automata."
A very nice aspect of Definition A is we can very easily check whether a given grammar satisfies it or not. We just look at it, and we know. This goes horribly wrong if we were to adopt Definition B. There is no algorithm that takes in a general grammar and tells us whether or not it defines a regular language. The reason for this is that we can translate Turing machines into general grammars, and thus eg produce a grammar that defines a finite language if the given Turing machine halts only for finitely many inputs, and some definitely-not-regular language otherwise.
We also wouldn't get any of the other benefits that right-linear/left-linear grammars give us, such as easy parsing.
