The short answer is no. Other image processing software will suffice for post processing of digital images. The more correct answer and the one I hope to support, is yes it is very much a necessity. Photoshop is to digital image processing what a chemical darkroom was to film. Photoshop is nothing more than the updated tool of the trade for modern day photographers, nothing more and nothing less.
Those of us who shot film were considered “Real Photographers” only if we were in complete control of our print making, at least that is what American Photographic Society rules for print competition told us. A real photographer uses his skill with lights, camera, and post processing techniques to regularly produce images beyond those of the average person that picks up a camera and clicks away. There used to be arguments over which film was used by “true” photographers, slides or negative. Slide film had less latitude and those who shot it often considered themselves superior to those of us who shot negatives. Publishing images was cheaper from slides than from color negatives and that is why photographers for major publications used it. Art photographers and print makers often chose negative films because of the degree of extra control they offered. The final product is what dictated choice of film in most instances.
All the talk in various forums about JPG vs. RAW essentially covers similar area. JPG images in the camera have been initially processed to the standards established by the camera manufacturer. For those feeling smug because they still shoot film and then scan images from their medium format slides, if the scanner is producing a JPG, your image quality is determined by the scanner manufacturer, not you. RAW images are processed in accordance with the standards set forth by the photographer (or post processor). Both methods produce usable images, but only one of them places all control of its outcome in the hands of the photographer.
Purists these days talk of not needing Photoshop. Most of them, talk as if they were a slide shooter in the earlier times trying to feel good about getting it right in the camera. If all they were doing was creating images for slide shows or no a days for web use, getting it right in the camera will produce a usable image. Good images for slide shows or slide competitions were often processed to lessen contrast because when you duplicated them, contrast was increased. Printing those images directly will often produce usable pictures. But, very, very few of those images are going to be so great right out of the camera that no further adjustment could improve them. Getting it right in the camera is the first step in the journey, producing a good print is the last, the in between steps are done using the tools and techniques that the photographer likes best.
Having good skills in Photoshop is at least as important as knowing how to print your own images was to photographers that used film. It didn’t matter if you printed from slide or negative, you still dodged, burned, tweaked the color controls, and did any and everything you could do to regularly produce your best work on paper. If you got good at it, people would ask you to print their work for them. Good print makers are not always the best photographers, but they constantly look for tools and techniques that make images easier and better. Photoshop gives you a set of tools for use with digital image files along with others that make your workflow much faster and better than chemical darkrooms ever could. Good photographers will use these tools and continue to produce images we love to see.
Getting it right in the camera is the first step in the journey, producing a good print is the last, the in between steps are done using the tools and techniques that the photographer likes best.