There is a photo school teacher in the Chicago area led by Will Crockett called Shoot Smarter Not Harder,
www.shootsmarter.com. Several years ago while teaching a class, students were editing and erasing individual images as they shot. When they tried downloading into the computer, the entire card was corrupted and everything was lost. In fact the card was worthless and had to be thrown out.
Personally, I have not experienced this problem and occasionally have erased individual images as I shot.
I still do not recommend erasing on site and prefer to wait until all are loaded onto the computer and erase on the computer. I shoot for a studio and I manage the files on the computer. Some of the other photographers have been at a dance photographing couples. As they shoot, they may notice someone blinked and take another shot and then erase.
Unfortunately, I find that the photographer has erased both images of the one couple leaving me with nothing. Or, they the other person blinked on the second shot and he/she did not catch it. If I had both, I could have transferred the open eyes from one photo to the other.
Sometimes, on the tiny screen of the camera (even though they may magnify the vue) they miss something, or due to the pressure of time while trying to shoot many couples in a short amount of time at a dance, mistakes are made.
Then there is the story of a famous wedding photographer who was givin a digital camera by a major camera maufacturer to test out before going to production. He found two problems; one with the camera and one with himself. He went to erase a photo by pushing the button and nothing happened. He pushed the button a second time. Well, this was one of the first pro cameras and it had a slowere processor. If he had waited it would have eventually erased the photo. But, pushing the erase button the second time told the camera to erase ALL the photos. Thanks to his testing, this is no longer a problem with cameras today.
The other problem is that he spent so much time looking at the photos and editing that he was missing many other photo opportunities.
My conclusion, with the large cards available today, the speed of cameras and computers, and the possiblility of human error, it is better to do the editing after downloading onto the computer. If you edit after downloading and accidentally erase the wrong image, it is still on the camera card.
There is a photo school teacher in the Chicago are... (