In terms of hand-held photos of static subjects with prime lenses, you are correct.
With IS zoom lenses, you are not. For landscape and architecture zoom lenses mean you never have to crop. Unless you have no limitations on camera location, with primes, you could have to crop. On the other hand, primes typically have superior optics compared to zoom lenses. Computer-assisted optic design, improvements in manufacturing processes and post-production software corrections have reduced the gap. But it is not zero.
The DOF part is complicated because DOF also depends on subject distance. Now the focal length (angle-of-view) is another variable,