The reason I got into Cricut machines in the first place was to cut out miniature paper houses, rooms, and other miniatures that crafters had to cut out by hand. The pages for projects for sale were usually so intricate that cutting by hand could easily destroy the products, which were printed out on light cardstock. No computerized files just 10 years ago.
An example is from one of the major producers of videos on Youtube. She also has very comprehensive website with many projects, but it is a membership site with a fee. Here is an example to view: Click HERE
For a Youtube tutorial on cutting basic designs like flowers on cardstock, click here
Another fun thing to do is make greeting cards. Cricut even has an device called The Card Mat and materials to use to make cards for all occasions. For some examples of this project, click HERE
You can also make cards just using cardstock. Click HERE for another tutorial.
There are so so many things you can make with paper. Check out the Youtube videos for all kinds of projects.
And, there are other things besides paper. Look around.
Ed