What I am trying to say is that even if computers are going to be able to solve todays database design problems (which I am sceptical of by itself) - we are going to have bigger/more capable databases and other problems that computers are not able to solve.

It is going to happen by definition - people by definition want more than they have today and want to solve unsolved engineering problems ("problems" that machines can solve are simply not problems anymore).

The only way it can end is creation of some overwhelming intelligence (AGI) that would govern (or some might say: enslave) people so that their demands are controlled.