Obviously a full time class such as what is given to military divers and scientists can do the above, I am restricting my thoughts to recreational SCUBA only here.
I was as well. I'm not suggesting that the diver has to be 'completely trained,' as we all continue to learn. I do however think that they should be taught and examined to ensure that they possess the knowledge and skill-sets that they need to dive independently as a valuable member of the buddy team. One of these is some rescue skills (for example) which are omitted by some training agencies.