I think that's the thing, you really need to stab yourself with real force at the correct target area, and it's generally not something our SI allows us to do. Cutting is different, less forceful, we tend to only hit surface layers and tendons. Stabbing takes a lot of willpower and is very violent, hence we generally only see reports of accidental deaths this way rather than suicide.
I think even if mustering the willpower to stab myself that forcefully it'd then be down to luck whether I actually hit the target vein.
And it's something I've thought about in the past given my history of high pain tolerance to cutting, but I don't think I'm brave enough and my thighs are too chunky to locate the artery anyway so I'd have to go full on slasher on myself with repeated stabs.