Life, given right conditions and enough time, seems to be about as inevitable as the eventual appearance of viral cat pictures on online forums, in other words.
I think there is little wrong with assuming that the probability of emergence of life given right conditions and enough time is one; however we need to be very careful with estimating how common (and how stable!) those conditions are in our galaxy in the first place. A good place to start would be to look at how many places similar to Earth are out there (which we are already doing).
Fair enough. It's a bit like the infinite monkeys in infinite typewriters scenario. Given enough time, sure, you'll have life. It's a question of how much time. Still, assuming all Eart-like planets will actually develop life given the time lapse of the existence of the Milky Way does still seems like a bold assumption.
Your point is correct, but my hunch is that the time needed is no more than a million years or so (small on the galaxy scale), possibly less.