For what its worth:
A tie is not essential for a smart appearance, as has already been stated. As mentioned earlier as well, the heat of a 150 cockpit in summer (assuming we get one :-( ) would make the wearing of a tie very uncomfortable and fatiguing. That cannot be a good thing.
How about this argument for the banning of the tie:
They are definitely a loose article hazard.
Scenario: During exagerated 'unusual attitudes' the cussed tie wraps around the control yoke, and then the pilot repositions his hand on the yoke and trapping the tie in position. Potential control restriction during a period when full control is required.
Ok, my example may be a little far fetched but many workplaces ban any loose clothing and trinkets on equally flimsy safety grounds.
BAN THE TIE!!!