You are confusing thought experiments with reality. A thought experiment is under strict specific assumptions; it does not matter if reality looks different or this cannot actually be.

For example: "if I flip a coin once a second for all eternity, I will get heads at least once"; humans not living for eternity, the coin very slowly ablating away, the sun possibly swallowing Earth some day, or everything being turned into paperclips by a rogue AI don't matter and are not viable scenarios for this. They are idealized away, ignored.

They are usually done to either explore and understand some concept, or to show effects (paradoxical or not) of extreme settings, or are just a kind of game for its own sake. Like a science fiction book.

> Over an infinite period of time the probability of the universe ending is 1, right?

There is no physical reason for this to be so. It might be, but we are definitely not certain about it nor the opposite.