Not entirely clear on what you are asking. Do you mean you cannot delete the assignment of categories to non-custom category groups? If so, AFAIK there is no way to do that other than to create new custom category groups, and assign categories to them.
AFAIK, there must be category groups, either the default ones (that apparently don't work for your purposes) or custom groups(which can have whatever categories you want included).
@Permutations To change a category from a business group to a personal group, you must remove the tax line assigned to that category. Likewise, if you want to change a category from personal to business cateogry group, you assign a tax line to that category. Go into Tools>Category List, right click on the category of choice and Edit. See image.
You cannot delete Quicken Standard Categories Groups, only add custom category groups, as you wish.