But it’s not a model at all. If your point is that the patterns of gene distribution can’t be explained by any model we have shown, it doesn’t follow that your favorite notion is correct or even to be preferred. To do that you would need to show, at a minimum, that the pattern is to be expected as a consequence of your notion. This you can’t do because your notion has no consequences, at least none that you are willing to acknowledge.
And of course our model, common descent with branching, i.e. a tree, does explain the pattern quite well. As has been pointed out, your “waiting time” objection is both irrelevant, because the cause of fixation is not relevant to the pattern, and wrong, because it concerns particular events, not just whatever we happen to see.