Question: How does one go about building a page in wordpress that contains a contact form full of custom fields, boxes, inputs, etc. completely determined by the author of the site. It seems odd that wordpress currently lacks this feature, but knowing the wordpress community, it's unlikely that we must do without.

Answer: 
Add me to the Gravity Forms supporters list. Of course it does a lot more than just contact forms. You should definitely check out the feature list and decide if it is worth your $39 dollars. It was a no-brainer for me and I bought the unlimited site developer license. The time that it saves me makes it worth it.
Plus one for gravity forms as I have found it to be much easier for my clients to use. Is easier to provide theme support for (ie Easier to customize via CSS) and has fewer conflicts with other plugins