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: 
See the different- for only a form in one page it is easy and fast (no filter-hook or other) to write a template for a page in WP, for more flexibilty and functions us a plugin. A ready solution or a starter there you can find here: <https://github.com/bueltge/WP-Contact-Form-Template>
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