You’re welcome to transmit your own bank account details, routing numbers or whatever in any way you wish. But you probably wouldn’t send your friend’s or your work colleague’s bank account number in a clear-text email. (Or would you?)
What about discussions and private details about their personal lives? If you were discussing a cousin’s difficult personal situation with a close friend, would you want that private discussion to be read by a bored system administrator looking for a laugh? Would you want it archived and data-mined by Google, or some other marketing outfit?
If not, invest an hour or so to learn PGP or GnuPG, and use it.