As someone whom has trouble expressing their feelings, I find it very very difficult to say ‘I love you’ to my friends, my parents, even my sister. It’s something that I’ve always felt and wherever it stems from, it has a powerful hold on me. I think it’s the same for Bojack.
If he died, there would be no opportunity for him to turn himself around, nor any opportunity for him to reckon with all the wrongdoings he has done throughout his life. It would completely tear up the established moral of the show.