I personally think it's important. It is our way of showing respect to the creators of the martial arts style we study.
Craig T. Metzger
If you wish to study Martial Sports (i.e. the various 'styles' of MMA, kick boxing, etc...) then you are learning what works in a ring or octagon or on a mat for your selected sport. The only 'tradition' needed would be the traditions of the sport.
If you wish to learn Martial Science (i.e. MCMAP (Marine Corps Martial Arts Program), SCARS (Special Combat Aggressive Reactionary System), Krav Maga, Systema, etc...) then there is no real need for tradition.
However, if you wish to learn a Martial Art, that is to say a 'traditional' system of skills used for combat, physical, mental, emotional and spiritual development, then tradition is quintessential to the process.
Tradition is the difference between a soldier and a warrior; a trainer and a coach; a teacher and a master.
There is a great deal of wisdom and power in what was passed to you. How could you deprive another of the same conscientious dedication if you are a product of it? Respect in martial arts means more than the series of petty sacrifices one makes as courtesies. It also means respect for the self and ones own essential dignity.