"Cameras, by design, also introduce a level of distortion": distortion is an artifact that is usually minimized in lens design if you are trying to create a rectilinear lens, though you are typically forced to trade it off versus other design criteria (like resolving power, or optical complexity). If you're trying to design a rectilinear lens, you explicitly try to remove any distortion; for "normal" focal lengths (focal length ~= image circle diagonal) you can often get vanishingly low distortion, even with relatively simple lenses. (There was a 19th century lens design that achieved "zero" distortion with just a few elements, and a precisely-chosen aperture position; the name escapes me at the moment.) If you are not designing a rectilinear lens, there are other lens mappings, in which case it's not really proper to describe the effect as distortion, though in technical literature it's often still described this way. (For further reading, check out F-theta vs. F-tan-theta lenses: https://en.wikipedia.org/wiki/Fisheye_lens#Focal_length; https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=10....)
"... the proportions of objects closer to the edges of the frame are distorted." This is technically incorrect; objects subtend the same number of pixels in an f*theta fisheye image whether they're at the center of the frame or at the edge, for a given camera-subject distance. The apparent distortion exists because you're viewing it further away than the focal length implies, so the viewer at a "normal" viewing distance is applying a transform to the image that is not distance-preserving. If you get extremely close to the image, and if it were displayed on a curved surface (so the image's angular extent to the viewer matched the camera's FOV), you'd see no distortion. Also, we think of arranging subject matter for, e.g., a portrait, along a plane that's orthogonal to the camera's axis -- but then people closer to the edge are farther from the camera, and would naturally appear smaller. It's a weird artifact of rectilinear lenses that they're actually magnified in the resulting image so people standing in a line are all equal size; to get the same effect with a fisheye lens, you just have people arranged in an arc centered on the camera. (Most portraits are not shot on fisheye lenses though, for very good reasons, so this is more of an edge case.)
Related: "there are no straight lines" -- if you're using a camera to make an image, you're operating in projective space. Whether a line is straight in 3D space, and is then straight in the projective space, is a function of your projection. Rectilinear lenses -- for which the relation f*tan(theta) applies -- straight lines remain straight. But for most (all?) other mappings they do not; for example, f*theta lenses preserve angular extent: an object that subtends a particular angle from the camera's perspective will occupy the same number of pixels regardless of where they appear in the image. This is arguably superior for many computer vision tasks.
... I need to stop here, because this is already getting tedious. For anyone interested in developing a deep intuition for lenses and imaging, I would recommend playing around with a view camera, understanding the Scheimpflug relationship (https://en.wikipedia.org/wiki/Scheimpflug_principle), and really thinking through imaging from first principles if you want to understand these things more deeply.
Or just, you know, use Colmap and don't look back. That works too.