Admittedly, am layman, have only heard numerous sciencey folks talk about it, but we've found all these basic components in space already, naturally occurring, and while we've never to my knowledge recreated actual, genuine abiogenesis, we have observed every process required for abiogenesis to be a reasonable explanation for the origin of life.

As to your question on we should see the formation of new life everywhere, well, if we looked hard enough we might? The answer is competitive exclusion. Abiogenesis would've occurred on a remarkably clean earth: any life now emerging from the proverbial space dust is both almost certainly not preconfigured for this biosphere, and is instantly drowning in competing microorganisms that are. Anything that does form is likely quickly killed either by natural forces or competing organisms. Meanwhile, our life goes everywhere: We've found living bacteria on the outside of the ISS!