Yes automatics has improved the accident rate overall but three questions.
1 - Since say 1985 how many accidents have been caused by people keeping current with hand flying skills (I cant think of one). Please dont use people taking the auto pilot under totally inappropriate high workload situations (a la Kegworth).
2 - How many accidents have there been with people relying EXCLUSIVELY on the automatics (Several have already been mentioned).
3 - This cannot be answered numerically as there are no stats but how many accidents have been avoided by at least one of the two guys up front being able to cope? Be this with a landing on standby instruments (electrical emergency), exceptionally strong crosswinds (in compact old Europe most destination alternates will be affected by strong crosswinds and it is not that easy to avoid them). Not f/o bashing btw as in my company I know of a situation where the Captain bottled it and insisted the f/o to make the approach and landing. F/o subsequently bullied into keeping quiet. Yes I know he should not be flying...but he keeps passing in the sim.
No it does not hapen often; but a professional needs to be able to say that if it does hapen once in 45 years I will be able to deal with it without stress levels going ballistic and all that this entails.
We all passed an IR but flying is a degradeable skill and, as I said earlier, the CAA are now very concerned that ths skill is being lost. Just because you can jump through hoops and fly a single engine ILS with a flight director every six months does not make you a competent pilot.
Bottom line be good at both. Practice manual flying in appropriate conditions.