You have hit the nail squarely on the head. In fact, it is probable that most pilots would be delighted at the opportunity to have that sort of practice. If pushed by ICAO - and by association by regulators - it would surely increase pilot handling proficiency - particularly of newly graduated low hour first officers now being steadily recruited into the airlines. More simulator training as suggested above would also reduce the insidious slide into automation dependency. It would be money well spent.
I am with you on this, but there in lies the rub. The airlines DO NOT WANT to spend the money on unnecessary, i.e. not required training. If I was a chief pilot I would demand my pilots were proficient at these skills and allow them to perform them on a daily basis. That's how I learnt and still keep those skills even with FD on. You have to scan the basics to ensure the FD is not telling porkies. I'm sure the FD's were beautifully centred when Turkish Airlines stalled at AMS. In todays airlines, where visual approaches are discouraged for 'safety issues' and to reduce the number of screw ups and G/A's = time + money, it will take a massive change of culture to shift back to basic piloting skills. There is no will, so there will be no way. And there will certainly be no extra sim training allocated to such frivolities. Meanwhile survivable crashes will continue and Air Crash Investigation on Nat Geo will thrive much to our frustration. One of the latest scenarios was survival if only basics had been employed. If they'd never been taught nor practised then the smoking hole is inevitable.