This approach would also potentially mean that they would lose the protection of the DMCA which in their position as hosts of content, rather than providers, means will only be liable for copyright infringement if they do not respond to a takedown request. If they vetted each and every app and one slipped through which the store holder should have rejected as being an infringement then they would potentially become liable.
As a result, the onus is on IP owners to contact the stores to request takedowns. Unless an IP owner is actively scouring the stores, this may result in copycat apps remaining up. Yes, it may degrade quality, but this is preferable to the above alternative.
They probably don't strictly "allow" it in many of the cases cases that occur, and neither does the law. The issue that the store owners aren't able to effectively actively police it, and it relies on the vigilance of owners of the original apps to identify and complain of violations. And even most app owners have more productive uses of their time than hunting down every clone that might break the rules.