I think proving something like this is unfeasible. What is shown in studies of expert performance is that there's a very strong correlation between the hours of deliberate practice and expertness in some field. That is, pretty much without any exceptions, experts in any field have been practicing for thousands of hours, the number typically quoted is in the order of 10000 hours. This doesn't prove anything particular about the necessity of talent, but it proves that at least hard work is necessary.
But, on the other hand, nothing in these studies suggest that some talent-like property is necessary.
That Dweck book is indeed a good one, if not a bit touchy-feely in its take. It's really important finding in Dweck's studies that this mindset distinction has a huge effect in the effort people make. The people who believe they're bound by their inborn talent (fixed mindset) do not push hard and usually just give up when hard problems come up. People who believe the opposite (growth mindset), that your abilities are not constrained by your inborn talent, tend not to give up when things get difficult but just put more effort until they actually do manage to solve their problem.
So, in this sense it's actually irrelevant whether or not inborn talent is necessary, because the mere belief that it is could have negative effect on your effort.
But, on the other hand, nothing in these studies suggest that some talent-like property is necessary.