Your assertion seems true only if subgroups can maintain a positive growth rate indefinitely, which is theoretically possible but hardly proven, particularly a

Your assertion seems true only if subgroups can maintain a positive growth rate indefinitely, which is theoretically possible but hardly proven, particularly as history show that subgroups that grow too much splinter, and the splinters do not all maintain the parents growth rate. Most splinters dwindle, so a simple exponential growth does not apply for long. (On a global scale.)