I'm guessing to distinguish it from other moods. The subjunctive mood does sound very old-fashioned though, and most people never use it.

Basically, history. A form of "were" was used as subjunctive long before we used it to make past plurals. You can use "if I was" to mean a subjunctive form, but that's no excuse to ignore "were".

The SUBJUNCTIVE MOOD was used in Old English, but Modern English has only retained the "If I were" form of the subjunctive. You will also hear the " If I was " form frequently.

I'm not a native speaker, but I'd like to point out that you may use was for first-person singular and third-person singular sometimes in informal occasions, except "if I were you,..." And I don't think this mood is that old-fashioned because I hear it in American movies and TV plays from time to time. Maybe it depends on where you live.