It is too much to hope the individual companies to start solving the problem as many are of he opposite philosophy. It's a sad future in the short term.
This has to be done by regulation.
If margins are tight and the company sees this:
Automated sector: Fuel used 2,305 kg
Partially hand-flown sector: Fuel used 2,357 kg
The accountants see that 52 kg they multiply it by the number of sectors the company flies a day and decide that hand-flying costs their company £X.XX per year.
Safety arguments are dismissed by the comfort of knowing that if lack of ability to fly does cause a crash, it will likely to be the other guy's plane which will crash.