To me the only real problem with copying each others spellbooks is the "other stuff".
A spellbook is much more than a magical version of your mom's favorite Betty Crocker cookbook. It is their list of spells yes, buts its also research journal, note pad, and personal diary. Let someone else copy spells without close supervision and you are giving them a complete all the warts included tour of your mind, goal, and souls.
Ever mentioned to your DM that your LN wizard is would love to become a Lich? Then you can be sure there are the occasional notes in you spellbook as you have considered the process and what it may take to accomplish. Let your buddy wizard borrow your book to copy spells and with enough perusing he will come across mention of your desire for undead power.
So no, there is no game mechanic reason why it cannot happen, but there is a some role play trust reasons why someone may hesitate.