Except if that were the case why hasn't JASON killed the Joker by this point? Trying to make Batman do it is past "necessity" and into "ludicrous"
1)Because love (even filial love) makes you dumb. Especially when you are a teenager. Jason is all "you didn't love me! you forgot me! PROVE IT TO ME THAT YOU LOVE ME, GODDAMNIT!" because, to him, getting Bruce to prove his love is more important than anything else, even than his own life.
2)Because in the DCU nobody can kill the Joker ever. There is a reason the trope is called "Joker Immunity."
And yes, that's ludicrous. I freaking hate that trope.