Cold brew really does need to be forced through an Aeropress though doesn't it?
I tried dripping mine through my usual fine mesh sieve, and it just got clogged.
I suspect that the coffee flavor oils are solid at cold temperatures, and clog up the holes so that even water can't get through.
And I wind up with a thin puck of very fine particles at the end of the pressing. No doubt a lot of solidified oils are trapped too.