The timer mechanic is to give the player the sense that he is not the one and only person in the entire organization who is actually doing anything. You give orders to a dood, and he says OK and goes to do it, and then later he comes back and says I did it. In the meantime, you are supposed to do other things, not just sit there and stare for 6 hours
Take out the timer and those support characters just become ATMs - push a button to instantly receive cash and influence. That would be much stupider. As to the people who cheat by resetting their clock - you know the dev console is right there, right? Why not just give yourself a billion influence and call it good? Seems weird to me.