There is way less bandwidth involved since the amount of data transferred for a shared coding exercise does not surpass the data (pixels) involved in screen sharing.

Helps with remote interviews/candidates with slow connections.

I think screen sharing isn't really optimized for text legibility - it's still the same video calls, just using screen capture instead of webcam as a source.

When I've shown some code over Skype, I had to change fonts size to pretty large to make sure it was comfortable to read.

Also, bandwidth. Video streaming requires a lot.

I don't have a legibility problem using TeamViewer, done a lot of pair programming this way.