AFAIK Boeing only recommended NOT deselecting as often 737 was first jet type for turboprop operators so KISS...all manual or all auto.
I was unable to locate that additional "advice" you quote (?) from the Boeing 737 FCTM about "as often 737 was first jet type for turboprop operators so KISS..all manual or all auto". Someone has been pulling your leg, methinks
The FCTM does state: The autothrottle ARM mode is normally not recommended because its function can be confusing. The primary feature the autothrottle ARM mode provides is minimum speed protection in the event the aircraft slows to minimum maneuver speed . Other features normally associated with the autothrottle, such as gust protection, are not provided. The autothrottle ARM mode should not be used with non-Normal Checklists. Some malfunction that affect maneuver speeds cause the autothrottle to maintain a speed above approach speed.
If your company chief pilot wants you to use the ARM mode for approach and landing, then he would be wise to contact the manufacturer and request their advice. In turn the manufacturer will likely say read your FCTM or maybe even "fill your boots" and quietly advise your insurer on the side
