Surely recognising that the aircraft has departed from controlled flight *is* a handling skill?
Recognition is a management skill, recovery is a handling skill
In both the Air France and the BA Staines accident the pilots did not recognise what had caused the loss of control yet all of the pilots possessed the handling skills to recover the aircraft as would any PPL student with around 10 hours dual.
You do not need to practice handling skills regularly to be able to move the CC forward when you experience a loss of control but you do need a through understanding of what can make an aircraft not respond to normal control inputs by way of Threat & Error management