In the one Dawkins book I read, the mathematical part definitely gets addressed. It may change your mind about the mathematical part.
I once read elsewhere that almost all the specific details Darwin came up with have been overturned by other scientists. But the new scientific results prove evolution and natural selection even harder.
My own personal speculation is that there may be many simple proteins that have some type of use or another. I would be interested in reading about how they came up with that 10^77 number. Sounds high to me.
On the other hand, I've read scientists make comments similar to your comments. Not in papers, but in casual interviews. Some agree with you and say that even given the current theories, there just wasn't quite enough time on earth to create life from non-life.
It's not an accepted scientific theory at all. More like a crackpot idea that will probably never be proved or disproved. But take a look at the panspermia theory. Small seeds of some kind move from planet to planet. Maybe one landed on earth long ago? It's a crazy idea. But it does address the issues you brought up.