If you have a website mywebsite.com, you better well allow people to type in "mywebsite.com" instead of just www.mywebsite.com!
Every time I come across some company whose website address doesn't work without the "www", my confidence in their ability to do their real business goes way down.
You have to dot your I's and cross your T's in today's world. Because if you don't, someone else will. All things being equal, I prefer to do business with companies that seem to be on the ball with everything - especially the customer facing portion of their business.