I am a person who always prefers the community over the gameplay and stuff. And from this game's target audience ,which are horny people XD, a chat system would be a great idea for this game.
Firstly, if you been to certain online chat systems (sex chat servers, omegle, etc) you'll see that they will always be these kind of people around. By adding a chat system, these horny people will have more fun and possibly allow more horny people in this game.
Secondly, There is'nt a way to pass the time while waiting for your missions to finish. While you can talk to your studio members, it's just limited to your studio members. So instead, why not just talk to random people on the internet. You can have weird conversations to people if you want XD
Thirdly, The mail system aint that effective when it comes into making a conversation towards someone. Usually, you send it and you wait for the other person to read it. Since they dont rly expect any mail, it's gonna take a long time for u to get a reply.
Just consider about this idea and i hope that you add it into the game