No, it doesn't defeat the purpose at all, they would have no control over the currency, no ability to inflate it or change it in any way, because they are a single actor in the system.
How is the network being validated by over 200 CBs in some way inferior to having most of the work being done in China or the US....which is currently happening!
You must live under a glass bell where everything is ideal, there are no bribes, corruption, crime and bad intentions. Do you really think that central banks would play by the rules, who would set those rules at all, maybe you?
The belief that CBs would play fair and not change anything is naive to say the least, because it's like saying that all the world's major powers don't cooperate on key issues - and that their influence doesn't influence others to play by the rules they set.
If BTC mining were to be managed by the central banks of countries that are members of the G20, for example - how long do you think it would take them to agree on some changes that they could definitely implement given that they control the network? You live in total delusion if you think that there is no difference between the network being controlled by those who just want to make a profit and those who are interested in some completely different things, because they have as much money as they want anyway.