I advocate more time with no FDs when circumstances permit. Indeed. But I also suggest four 4 hour sim sessions a year with nothing but raw data manual approaches, two engine go arounds with early level offs, unusual attitude, stall recovery and unreliable airspeed. Pure training, no checking, no marking, no records, no systems, no stress, just feedback and performed by TRIs and not TREs so as not to influence the actual checks.
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.