It doesn’t just cool the air, it removes moisture. That’s why it’s called air conditioning. Hence moisture from people’s breath will get removed.
Your “analysis” of the problems with recirc is flawed.
Running air from the AC over your windows removes window fogging, after all. (But it chills the windows so if you turn it off the fog returns quite quickly.)
AC removes moisture, hopefully everyone realizes that by now.
What you and others upthread experienced is vapor condensing on the glass surfaces which are colder than the air. The air reaches its dewpoint at those cold surfaces but generally not where air is moving over the glass by the air duct outlets…