Why birds do not fall while sleeping

AFAIK key insight into evolution is not randomness but rather sheer amount of compute. Specifically, evolution is a massively parallel flood algorithm that will try every single mutation. Barely any of them will have positive impact on organism fitness, but some will.

That, and of course the other key insight is the "flood algorithm" part. I.e. evolution isn't about randomness (the "throw some parts into a bag and spin them until a 747 flies out" criticism), it's about bias and feedback: the environment itself isn't uniform, creating a bias in what would otherwise be entirely uniform selection, one which compounds with every generation. Randomness is just adding variance here, jitter preventing the process from getting stuck with one outcome.

The way I understood evolution wasn't that "some mutations will have a positive impact", it's more like, when a species hits hard times, "some mutations allow it to survive long enough to reproduce".

Sure, you have dominant genes like eye colour. But evolutionary changes to a whole species are more about weeding out genes that cannot survive, right? Because if a species has no specific sexual selectors for breeding and all mutations survive and reproduce, then how does a specific gene thrive?

Edit: but chatting to my wife, she mentioned that species is a difficult concept, generally taken to be a generic group that actual mate in the wild. There are several different species that could technically produce offspring but through sexual selection, do not.

You will probably find this article about the species concept interesting:

https://plato.stanford.edu/entries/species/

Also worth pointing out that billions of years already sounds like a long time to humans, but once you grasp how quickly everything is moving at the cellular or molecular level then it becomes a really reallllllly long time.

Random factoid I picked up from The Machinery of Life: how do various proteins inside a cell know to find and bind to a specific chemical or protein they need? They don't - everything inside a cell just constantly bumps into everything else, and because of how fast things move at this scale, it doesn't take long for any single thing to touch approximately every other thing inside the cell. I.e. turns out random walk is a viable search mechanism at nanometer scale.

I remember early "computer recreations" of life that seemed to suggest that unbounded randomness (mutation) was, as you mention, more often bad than good. Sexual reproduction, where genes are swapped (perhaps at random?) got you to the head of the class much, much quicker.

And presumably the size of cells is partly determined by constraining enough of the right things close enough together, so they will bump into each other quickly enough with probability approaching 1.

Right! Cells larger than that stop working reliably and end up self-selecting themselves out of the future generations.

Now I wonder if internal structure of cells can be attributed to that too - i.e. organelles create zones where processes relying on fast random walk can work, enabling the cell itself to grow bigger.