Are there any countries in which post-dated cheques are commonly used in trade?
Iran is another similar case, however in Iran use of post-dated cheques are mainly due to difficulties that a businessman will face if he wants to use bank loans.
For example banks usually have a well-known precondition for extending loan to firms and households which is providing sufficient liquid collaterals.
For finding more theoretical elaborations you can search for "access to credit" literature which tries to elaborate why banks do not have sufficient incentive to provide credit to some people.