I was riding a dead onshore and a massive shore break around Biarritz with a Naish Fly. It works as long as you have enough power in the kite. Say, 12-14kt. Requires very active flying though and you n need to sine the kite before the whitewater hits you. The kite drifts ok but is too slow for fast top turns. For long clean waves it is ok, for gnarly shorebreak it is possible but just no fun.
So in onshore winds and big waves there will always be a problem of outrunning your kite. If it is straight on shore, it really depends on the wave shape. If it peels off nicely you can potentially keep enough pressure on your lines...if it is a closeout section, you basically head straight for the kite...and the bigger the wave the faster it is..but my point is that the days when you hit it right..the waves gets glassy...and the waves peel of just right it can still be a lot of fun