If a rep turned up wearing no tie and worst case carried his laptop in a ruc-sac, I got the impression he wasn't serious.
In a negotiation, of which all business meetings were to some extent, wearing a tie gives an air of superiority and its better that I have that than the supplier.
Re the funeral, wearing a black tie shows respect.
Of course, at a wedding, as soon as the drink flows, off come the ties, waist coats etc. you know, ready for the inevitable punch up when the girls have had too much to drink!