If that really is how life got started then it's likely that primitive cells are still being spontaneously created near these vents today
Modern conditions are very considerably different to those in which life developed on earth.
For a start, there is oxygen. Now, it may be true that oxygen is essential for large organisms to develop (we only have a sample of one ecosystem, in which oxygen is almost ubiquitously associated with large organisms ; but that's an "almost ubiquitously", not an "always" ; the case may be suggestive, but it is certainly not proven.), but we're not talking about large organisms, we're talking about the formation of the first very small organisms. For certain, life evolved on Earth for a very long time before there was any significant amount of free oxygen in the ecosystem. Life and significant concentrations of oxygen have coexisted at best for a half of the duration of life on Earth.
For a second thing, the modern world is full of organisms that breakdown ad re-use organic molecules. While there is a lot of debate about what particular compounds were common in the pre-biotic/ peri-biogenetic environment, it is sure that the modern environment has been stripped of many of the more complex molecules. Some of that stripping is due to the molecules being broken up by reaction with oxygen (see above), but much of it is simply going to be eaten.
The likelihood of life spontaneously developing around modern deep-sea vents (or shallow-sea vents, for that matter) is considered pretty low, even though their ancient analogues are certainly sites of interest for biogenetic models.
Radical re-thinking about the possible environments for biogenesis happens almost every time there is a new student writing a paper on the subject. There is not a scientific consensus on the question (though there are certainly ideas that are more popular than others). If this clashes with what you've heard on Discovery Channel, then I'd advise you to swap their (pretty shoddy) "journalism" for actually reading the relevant science. Much of it is available open access.