Mesaana in her arrogance probably considered the whole of Tower to be her private apartment. People need permission to take sa-angreal, and Mesaana would probably be the one deciding to grant it. She probably thought that the sa-angreal in that room was secure in her hands.

For the other Forsaken traveling into the Tower is probably a bit dangerous. With all the Aes Sedai around, they might get caught, and they would really be trespassing on Mesaana's turf.