It doesn't, really. All it takes is a single individual animal to carry a virus. The assumption that all of the individuals of a species harbor the virus is faulty, it could well be a small fraction of a rare animal, in fact the difficulty of locating the reservoir is strong evidence for that.
Sticking to Ebola for the moment: even though there were major suspicions that a species of bat was responsible for Ebola it took a very long time to identify which species and how Ebola managed to transit the continent and to pop up in different places.
https://www.nature.com/articles/s41598-020-71226-0
Reservoir animals can be very hard to determine with certainty. Note also that the reservoir animal itself need not have been present in the wet market for this to have worked, it is enough that a pig or some other suitable amplifier host got infected which then passed it to humans. In that case too, you'd see a small number of animals, possibly even a single individual, carry live virus. And given the nature of the wet markets you can be pretty sure that any such evidence was erased before COVID even had a name.
Until there is hard evidence for a lab leak I will chalk it up to a possibility, but a remote one. And if and when the reservoir animal is found I'm sure that too will be discounted by the proponents of the lab leak theory, who seem to have their bullet-proof fix already in the works: in that case the claim is that the virus was first sampled from an individual of the reservoir animal species and moved to the lab from where it leaked.
So we likely will never see the end of that, but that doesn't mean that any of it is true. Which is a problem with many conspiracy theories, they tend to be inherently un-falsifiable which allows them to stick around forever. The way in which one of the authors of the book effortlessly integrated new knowledge that invalidated the premise of the book into an altered version of the same - instead of admitting they got it wrong - is a very nice example of that.