Th e fungi is a great example. Maybe the problem isn't with death, but with life. For modular organisms like fungi, it is hard to define an individual, and even harder to define the lifespan of an individual. When you cut a fungi into two parts, does the original fungal lifespan end and do two more individuals with new lifespans prop up? Or do whe consider the two fungi to be one organism living out the same lifespan?
To get back to the topic, perhaps it is useful to think about why unitary organisms die. Let me propose that being unitary gives structural advantages due to its determinate growth, but a natural consequency of this is death. Death isn't directly evolutionarily advantageous, but it is a consequence of the vertebrate body plan and determinate growth which in turn has selective advantages.
So that this isn't completely hot air, here is a review article that claims determinate growth is common in vertebrates, and can have selective advantages in some situations. [
Just a moment...]
Unfortunately you need a subscription to access the article, it is rather old.