Your need to rezero in this case has very little to do with 18" to 16" barrel, and everything to do with installing a new barrel.
While there is a little velocity change for 18" to 16", it would hardly be enough to matter. But even if you replaced the 18"
barrel with another identical 18" barrel, you need to rezero. Just taking off the 18" and reinstalling it will change zero.
There is no way that a new barrel will seat in the upper receiver exactly the same way as the previous barrel. A very slight
change in the way the index pin goes into the slot of the upper receiver, the way the front sight base is mounted, and even
very slight bending of the upper when torquing up the barrel nut will all affect it.
This is also why you can't "memorize" or "write down" your sight click numbers and apply them to another rifle "to get your
personal sight in." Sorry, but every rifle is different.