Does it seem that way? It happened at least once (but could have happened many times without "taking over"), and certainly one sort of life seemed to successfully out-compete all others. But none of that says single-origin to me.
Early on I would expect a whole lot of "horizontal gene transfer" sort of things to have taken place. So for example in addition to actual horizontal gene transfer, there are mechanisms like one organism enveloping another to eventually become organelles, co-opting products from each other, etc. All of which would act to homogenize life and make certain process ubiquitous.
Finally, there's an outside chance that "there's only one way to do it".
Early on I would expect a whole lot of "horizontal gene transfer" sort of things to have taken place. So for example in addition to actual horizontal gene transfer, there are mechanisms like one organism enveloping another to eventually become organelles, co-opting products from each other, etc. All of which would act to homogenize life and make certain process ubiquitous.
Finally, there's an outside chance that "there's only one way to do it".