MIT/BSD licenses are essentially a copyright waiver.

They are not. You still have strings attached: the requirement of attribution and the disclaimer. With 3-clause and 4-clause BSD, there are even more strings attached.

You can't just take MIT-licensed code. You have to take the code and the full copyright notice and license grant with disclaimer.

Copyright law doesn't allow you to waive those rights without falling into Public Domain, which is considered grey area in some countries.