I'd like to address some issues that didn't come up in any of the previous answers.
In a comment, you said:
The cost to create a census is many times larger than what it would take to digitize them. It seems like digitization could be in the national interest - funded by the Library of Congress, for example.
The relative cost of digitization versus what it cost to produce the records in the first place is a red herring. Most, if not all, of the primary source material we use while doing family history research was not created for genealogical purposes. The census was taken by the federal government (most recently, by the US Census Bureau) for purposes of its own -- and we are lucky to have any census records to look at, because many censuses (e.g. Australia, Ireland) were discarded once their original purpose of creating statistics about the population was served. If the record creators don't have any need for the records to be digitized, there's no reason they should do it -- it's a waste of money.
Secondly, while the Library of Congress may have special collections of its own, it is not the primary keeper of our national records. Once records are created, they are owned by the agency who created them for a certain number of years, after which they are either discarded or archived. This lifecycle typically is expressed as a rolling window, often dictated by law. Privacy restrictions that determine who can access the records also may have a rolling window; custody of the records and restrictions on public access are two different issues. For records created at the Federal level, the main repository in the US is the National Archives and Records Administration -- often abbreviated as NARA.
When records are kept instead of being discarded, any archive has a limited budget for projects such as digitization. Imagine the path a record set takes as it goes through its life cycle. Starting with the point in its life when (if) it becomes archival, it might take a path like this:
- Records arrive at the archive
- Records are accessioned (cataloged and arranged in a form that allows them to be used by researchers)
- Records are designated as for public use or restricted (and may need to be hand-screened for privacy issues before they can be copied or viewed in the reading rooms)
- Records are (a) microfilmed or (b) digitized for preservation purposes (e.g. very high-quality microfilm copies or scans are made)
- Working copies of the films or scans are made for easier access to the records by the public (working microfilm copies for reading rooms on heavy-duty stock, or a website that can be accessed by the public)
- Indexing may take place so that the images can be searched for rather than browsed sequentially
Archives do not have unlimited budgets. Digitizing records for which working microfilm copies already exist takes away resources for making preservation copies of records that have not yet been microfilmed or scanned at all. It makes more sense for archives to prioritize making new images for preservation purposes for records that have not been copied at all over making digital scans of microfilms where good working microfilm copies already exist. NARA works with Ancestry, fold3, and other digitization partners so that we taxpayers don't have to foot the entire bill for digitizing records. You can learn more about their plans on NARA's website here: Digitization at the National Archives.
One project which has recently been funded completely, where the digitization is still underway, is the Preserve the Pensions project, to digitize the 1812 Pension Files. Preserve The Pensions says:
The Pension Records from the War of 1812 are among the most requested documents at the National Archives. Unfortunately, these fragile documents are in urgent need of digitization. After five years of hard work, the community raised more than $3 million to support the digitization of these important materials. In support of this monumental task of digitizing 7.2 million pages, Ancestry.com provided a dollar for dollar matching grant, so every dollar contributed will make four more pages accessible and free for everyone.
Note that the records were chosen for this project because they were 1) heavily requested and 2) fragile.
In addition to these large-scale projects that increase public access to records that are held by NARA, at Archives 1 in Washington DC, the Archives also has the Innovation Hub, space for members of the public to scan the documents which have been pulled for people to view for research. Archive users can scan the records and keep a copy for their own use, and the scans are made available to the public by uploading them and attaching them to the corresponding entry in the National Archives catalog. The Citizen Archivist program makes it possible for members of the public to transcribe, tag, and share the documents with others.
It doesn't make sense to go back and digitize the older census microfilms on a special site just so they can be free, when there are so many places one can look at the microfilms for free already, like the Internet Archive, the US National Archives' reading rooms, public libraries, genealogical societies, historical societies, etc. It makes much more sense for NARA to concentrate on preserving and filming the heavily-requested records that haven't been filmed yet.
Also -- the term public domain has a specific legal meaning in copyright law -- it is not a generic term which means "hooray I can access this for free". One of the problems with this question is that it is asking two questions in one -- the first about public access, the second about what is in the public domain.
In a comment about the Internet Archives' copies of the census microfilms, you said:
... do you know if these are complete or what the license is? E.g., could I post one of these images to Wikipedia or WeRelate.org?
Please make note of all the terms and conditions for any site you download images from. Questions about permissions -- whether you can use an image for a blog post, presentation, family history book, or other publication -- are different from questions of access. Ask for permission from the site where you found the image or to the holder of the original records, as appropriate. To get more general information about the public domain, one place to start might be the blog The Legal Genealogist, searching for the category of copyright. Russell has talked about the public domain, copyright, and permissions for use many times, so there is a lot of useful information and a wealth of citations to references on her blog.