I have a cup of tea in my main hand, and a biscuit in my off-hand. To claim that which hand they are in doesnt matter is simply ludicrous, if I attack first with my biscuit instead, there may not be any left for dunking.
On-topic, lets assume I actually followed all that..does it really matter? Everyone just equips their best in their main slot, and their second best in off-hand and thinks no more of it, unless they choose to change their attack animations. If there was no difference as the OP claimed, people would still be perfectly fine doing whay we have always done..
One of the reasons I always equipped my best dagger in my right, is simply because it is always the first to attack with auto-attack, and therefore is the important one when factoring in passives, like if you had to use a normal attack from stealth because your abilities were on cooldown.
Also, many people actually manually change their attack chain by chain cancelling with the run key mid animation - this often results in more hits from the main hand weapon (1,2,1,cancel,1,2,1..repeat)and an increase in dps - not sure how relevant this is to assassins though as its usually big two handed weapons I do this with and havent tried with assassin - though its certainly possible and worth doing if you only have one decent dagger.
Forgive me if I miss whatever point you are trying to make, but I do believe I have listed two specific reasons why equipping main and off-hand is important to me, and how it can affect my gameplay.