That's an interesting point, and I'm going to try take it a little farther:
Perhaps the reason most people think of "legalese" as something that is nigh unintelligible is because the vast majority of legal matters that ordinary people deal with are the sorts of law that are well-established, and have been for decades or even centuries, which means that the language used for these matters is often boilerplate from long, long ago.
When you get to novel issues of law, such as what the Supreme Court deals with (usually), or the cases considered important enough to be reported, you will still have to deal with (1) weird language when it comes to the procedure that lead to the case being in front of the court, and (2) the fact that a complicated set of facts often leads to complicated sentences.
But otherwise, the opinions are usually fairly clear. They are written in modern language, by a person who probably grew up in circumstances similar to your own. There is the occasional bit of jargon, but it's not like trying to read a different language.
As for the common legalese that people encounter with boilerplate language... I don't really know if there's a good solution to that.
And of course, I'm sure there is some truth to the idea that lawyers use their jargon to stay exclusive, but I think that's true of any profession.