Alternatively, are there any other problems to using this as a definition of kind?
Other than the fact that we see subpopulations become nonreproductive with other populations all the time?
We use the interfertility criteria as the definition of "species." The big problem is that we see new species all the time, so if kind = species, we're seeing new kinds all the time, too.
It's the only definition of "kind" that has any basis in biological reality, so in that sense, it's a great definition. Your friend will come to regret using it, however, because it's very clear that, under that definition, we see new "kinds" all the time.