A digital camera is harvesting light in front of the lens and takes it to the sensor. Rays bounced from what is in front of the camera come from any direction and are bent by the lenses to hit the image sensor. Those rays that are directed to the edges of the sensors have to follow a longer path than those that are directed to the center of the sensor. Not a big deal, less than a mm difference but this creates “softer” (i.e. less defined) images at the edge of the frame, sharper at the center. The lens tries to compensate for this by using several additional lenses, making the lens heavier (and more expensive).
That is why Sony in 2017 patented a curved sensor for C-size frame image sensors and in 2018 Nikon followed patenting a curved sensor for the full frame format. Indeed, a curved sensor would make lens design easier, the lens lighter and the whole cheaper.
No wonder that an article on Gear Patrol got excited about the potential for a curved sensor and goes as far as saying it might be the next big thing in digital cameras. Except that, in my opinion, it won’t.
Why? Well, just imagine replacing the -flat- sensor in your camera with the curved one. You would be able to buy new lenses performing better but, what about the thousands of $ you spent on your current lenses? They would no longer be usable, you would need to replace them all. Possibly there was a window of opportunity when the new mirrorless camera went to market last year. At that point you had to buy new lenses if you wanted to take advantage of the mirrorless feature so it would have been easier. Yes, the mirrorless cameras came to the market with an adaptor to make the old lenses (the one you paid dearly) working on them, but I guess (although I am not sure it would have been feasible) they could have built a different adaptor to compensate both for the shorter distance to the sensor and the curvature of the sensor.
Now I have the impression it is too late for that. Besides, in the coming years we are going to see the uptake of computational photography, with software taking care of fixing several lens problems.