I had a boyfriend in high school commit suicide. He didn't leave a note. He seemed really happy and had a lot of good things going on in his life, and everyone was shocked. It was just a couple of months into the school year, and the evidence was that he had been planning since the summer.
It deeply impacted me that he didn't leave a note. We hadn't gone out that long but were in that mad rush of new love and it was total cognitive dissonance for me that he didn't leave me a note, we wrote each other notes constantly (this was way before computers let alone cell phones). I can only imagine how his parents felt. In the early days of magical thinking, his mother told everyone he'd had a bloot clot in his brain. Eventually his parents divorced as often happens because parents tend to blame each other.
It will make things much easier for your parents if you leave them a note explaining why you made that decision. It won't make things good, of course, but it's far, far worse to wonder and never be able to know. It's not just knowing they weren't to blame, but what was the cause.
As far as the note being a reminder of your death, there will be so many reminders. The absence of a note will remain with them, I think, far more strongly than a note.