There's no question that a good screen will provide a better quality image than a "plain" wall. Having said that, I have a wall painted using a Sherwin-Williams super-white paint which has a very neutral colour and good contrast. I put a 110"-wide 2.35 aspect ratio black frame around it and the result is excellent, certain better than the cheap screen which have a visible surface texture and dubious colour neutrality.I have the image projected on white wall for more than a week now and I'm quite satisfied with the quality. I consider to get a screen to get a even better image, but I've seen some videos on YouTube and some comments say that the screen is not necessarily better than the wall.
The main draw back with a painted wall is that it's hard to make it perfectly smooth, unless you spray-paint it. However, the slight "orange peel" effect is noticeable only with light coming at an angle, which is not the case with projected images.