Example: Recommended way to hide entry fields in new contact view
One way to simplify data entry is to consider using a Profile as the way for your users to add new contacts. This means you add fields that you want, rather then removing fields you don't want. Once you have created a Profile you can then use the 'create' version link such as 

http://d46.demo.civicrm.org/civicrm/profile/create?gid=1&amp;reset=1

but you don't get the same warnings in terms of potential matches, and there are no doubt other downsides (such as the unwanted fields still showing on the Summary screen), but it may be worth a thought as a temporary fix if you hadn't already considered it.