In my understanding suffering -- craving and aversion and all which it results in -- exists in living beings to help sustain procreation, evolution, and life. Can the ideal of all beings attaining liberation, enlightenment, and thereby ending existence, then, be equated with the aspiration of the end of all life?
It certainly seems that the cravings & aversions that result in suffering are also the instinctual or underlying tendencies ('anusaya') that exist in living beings to help sustain procreation, evolution and physical life. This seems to be why the biological life of both animals & people involve the struggle for survival, the merciless devouring of the weak, wars & emotional heartbreaks, such as mothers mourning for their lost sons, children & family members killed in war.
It may seem like a contradiction but the Buddhist way of life has its foundation in harmlessness & thus the preservation of life. Where as the biological evolutionary life that includes cravings & aversions (but which also must include love & social co-operation), as already mentioned, often demonstrates a scant respect for life.
For example, in fables for children that later appeared in cultural Buddhism, there is the story of the Buddha in a past life deliberately & compassionately feeding his body to a starving tigress (female tiger) that had just given birth to offspring. The female tigress devoured the Buddha-To-Be without a thought. This shows how the craving tigress cared less for (another) life than the cravingless Buddha-To-Be.
Therefore, the idea of attaining liberation & enlightenment cannot be equated with the aspiration to end life because the sole goal of Buddhist practise is to improve life by ending both mental suffering & animalistic cruelty. Buddhism is about spiritual/wisdom evolution rather than biological evolution.
What is called 'liberation' in Buddhism means 'liberation from suffering' (rather than liberation from life). To quote:
This unshakeable deliverance (liberation) of mind is the goal of this holy life, its heartwood and its final end (culmination). Simile of the Heartwood
To quote again:
I have been baselessly, vainly, falsely, and wrongly misrepresented by some recluses and brahmins thus: ‘The recluse Gotama is one who leads astray; he teaches the annihilation, the destruction, the extermination of an existing being.’ As I am not, as I do not proclaim, so have I been baselessly, vainly, falsely and wrongly misrepresented by some recluses and brahmins thus: ‘The recluse Gotama is one who leads astray; he teaches the annihilation, the destruction, the extermination of an existing being.’
Monks, both formerly and now what I teach is suffering and the cessation of suffering. MN 22
To quote again:
How can a fool gain gain the human ('humane') state...when there is no conduct guided by the Dhamma, no righteous conduct, no wholesome activity, no meritorious activity...where there prevails mutual devouring, the devouring of the weak...when they have not seen the Four Noble Truths...leading to the cessation of suffering. SN 56.47
In fact, enlightenment is equal to a higher or better way of "life", which is why, as shown in the first quote above, it is called "this holy life". Dhammapada verse 21 clarifies this:
21. Heedfulness is the path to the Deathless. Heedlessness is the path to death. The heedful die not. The heedless are as if dead already.
This is why a synonym for enlightenment is 'The Deathless'.
The destruction of lust, hatred and delusion: this is called the final goal of the holy life. SN 45.20
The destruction of greed, hatred, and delusion: this is called the unconditioned. SN 42.1
The destruction of greed, hatred, and delusion: this is called the deathless. SN 45.7
To quote again from MN 140 about the Deathless:
By overcoming all conceivings, bhikkhu, one is called a sage at peace. And the sage at peace is not born, does not age, does not die; he is not shaken and does not yearn. For there is nothing present in him by which he might be born. Not being born, how could he age? Not ageing, how could he die? Not dying, how could he be shaken? Not being shaken, why should he yearn?
To conclude, the ideal of attaining liberation & enlightenment cannot be equated with the aspiration to end life.
As for the ideal of all beings attaining liberation (which would probably end human life but not all life), this is only found in Mahayana Buddhism and did not exist in the original Pali Buddhism, as shown in the Uttiya Sutta. From the very beginning, the Buddha never believed all beings could reach enlightenment.
Out of compassion for beings, I surveyed the world with the eye of an Awakened One. As I did so, I saw beings with little dust in their eyes and those with much, those with keen faculties and those with dull, those with good attributes and those with bad, those easy to teach and those hard, some of them seeing disgrace & danger in the other world. MN 26
Can the ideal of all beings attaining liberation, enlightenment, and thereby ending existence, then, be equated with the aspiration of the end of all life?
I think the above presupposes that this is an ideal: that all beings should be liberated. Moreover, we don't really know how life springs -- thus, perhaps it may always do so regardless if there is already life or not.
And if we consider Buddhism doctrine alone, apparently the only known "exit door", the only way out of it is nibbāna. So, another way of seeing an ideal is that, ideally, the path to the "exit door" should always be there for whatever being that comes to be to choose to finally rest.