This is absolutely not correct.

And your reasons are.......?

What you said here......

FAOs are responsible for a variety of functions:
international students, partnerships with overseas institutions, student foreign study
opportunities, kissing the University president's ass, etc.

Parents have purposely sent their kids to schools that employ FT's. Therefore, the relevant FAO needs to get a white face in that classroom or face the wrath of the parents. The same may not be true for universities, but it certainly holds true for many middle/high school international departments.

Many FAO's go far beyond not 'relishing' dealing with FT's, I know several who actually hate it!
Even so, the need to get a FT into the classroom is the number 1 priority of many FAO's, especially at this time of year.