People who make contact prints from large format negs, generally engage in it for specific purposes. Most alternative processes must be contact printed, as they require UV light for exposure, and there exists no practical UV enlarger.
In these scenario, a larger image requires a larger neg, thus some of the impetus behind ULF (Ultra Large Format) cameras.
The aforementioned AZO and hopefully soon forthcoming Lodima contact papers are slow silver chloride papers, specifically designed for contact printing. The printers who use these papers do so for the specific abilities they find in the paper, notably, dense blacks coupled with an ability to resolve the finest details in the highlights, along with the almost unreal apparent sharpness of a contact print. A well executed contact print can appear almost three dimensional.
Almost any paper, however, can be used for contact printing, some work better than others. In the last day, I have posted an 8x10 contact print made on Polywarmtone titled "Spun Aluminium Lamp" Because the negative prints directly to the paper, there is no technical equal (IMO) to a well executed contact print in the analog or digital realm.