The only issue in doing this is the lead time from the time the customer expresses the desire to have the product to the time when she actually has it. High lead times could offset all the gains of giving a highly customised product. While a customer would love a personalised product, she might hate to wait to receive it. The key would be speed up the product / service delivery process and make it seem 'fun'.
It is close to impossible to allow the customers to completely design the products they want from scratch. 'Modularisation' works out here. As Yahoo!, I allow my customers to use certain modules on their home page, allow them to locate it on the home page and then probably configure a background. This is exactly how a Volkswagen Beetle is custom designed. Again, exactly how a Boeing Jumbo is made specifically for an airline company.