why doesn't the save and next button work from a grid edit report?

Grid edit lets you edit many records at the same time without needing to open them individually. Save & next would have nowhere to take you because there is no next record, you are viewing all of them in that report.

Save & next is used when editing individual records when you need to go to the next one in line of the report.

I realize that.  However, if I click the Edit button for a record in a grid edit report, (for instance when I need to see information that may not be displayed on the report), it would be nice if I could then use the Save and Next button rather than the Save and Close button.

That makes more sense. I think it just comes down to the differences in workflow between grid edit and a regular report. Most people will want to be returned to that report in grid edit mode because grid edit made sense to use on it in the first place. If you see a need for save & next you could just grid edit the ones you can and then leave grid edit mode and go individually for the remaining records with save & next. 

I think it is also possible to create a button to put on those forms that would let you save & next without using the native QuickBase button. I believe it involves some javascript. It might be going a bit too far for this though.