Due to TIME_WAIT, when the server wants to close a connection, isn't it better to tell the client to close it on their end?

Question

If the server wants to close a connection, the server will have to wait TIME_WAIT seconds before its able to clean up the connection. Whereas if you tell the client to close the connection, the server side doesn't wait TIME_WAIT seconds because the client initiated it after server tells it to. Therefore the connection is instantly cleaned up on the server side. So wouldn't it make more sense to tell the client to close the connection instead of the server doing it so you lessen the odds of out of memory issues on server?