This really isn't the case. Some banks provide free electronic transfers to account holders at the same bank and third parties they have agreements with (i.e. billpay).

It's quite possible when performing an EFT, for the sending party's bank to charge a fee and also for the receiving party's bank to also charge a fee. I'm speaking from experience.

Though free, EFT's aren't instant and, IMHO, require more coordination.