In the old days of Common Law, stare decisis really meant something. It was the law as it had been interpreted by numerous judges over hundreds of years. And that law, in turn, was based on divine law and common law.
Now, as you say, it means nothing but the latest judge's latest opinion. It's noticeable that liberals always plead stare decisis when it comes to their precious decisions like Roe v. Wade, but they ignore it when it comes to overturning hundreds of years of precedents in order to get with the program.
That's Scalia's point. In an age of arbitrary opinions, it means nothing any more.
And the need for it (at least on consitutional matters) has been largely obviated by the fact that we have a concise written Constitution, which anybody can refer to. Since past judicial decisions are, as Scalia says, evidence of the law, and are not the actual law itself, they're useful in determining unwritten common law. But they're not needed in determining the written Constitution that's sitting right in front of us, and was designed for the people to be able to understand.