With no advantage, and a very real disadvantage, knowledgable people will not accept Bitcoin IOUs in lieu of Bitcoins.
It is not clear you mean by "Bitcoin IOUs". When you write "people will not accept Bitcoin IOUs in lieu of Bitcoins", it appears that you are referring to some kind of currency. But obviously you don't mean that because there would be no such currency in the Bitcoin case.
Examples of Bitcoin IOUs would include: Bitcoin-denominated savings on deposit; and off-chain transactions.