There is an interesting article on page 46 of the May issue of Flying Magazine (American) concerning pilot experience levels. The author looked at accidents and the level of experience the pilot had before joining the airline concerned.
Whilst the pilots were reasonably experienced, they had joined airlines at very low total times and most of the hours logged were spent watching the aircraft fly itself on autopilot.
I flew two sectors yesterday and logged almost ten hours, of which only a few minutes were spent with a high workload or hand flying. Whilst 3000 hours of this would categorise a pilot as experienced, it would only be the equivalent of a couple of hundred hours of real flying in a piston twin.
The time for a pilot to build basic flying skill is before flying for an airline because afterwards they will only get weaker.