The provisions of CAP 371 make perfect sense in an airline operation, but maybe one reason why some other countries don’t want to adopt it is that these regulations ignore the needs and conditions of a sizeable sector of professional aviation: daylight VFR-only ops, especially single-pilot.
I’ve worked for several operators outside the UK whose governing bodies used CAP 371 as their regulatory text, and for us these rules were only just shy of a disaster. In day VFR work there is no disruption of a sleep pattern – when it’s dark you rest, you only work when it’s light, so there should be no need for early or late shifts. The important factors to consider are maximum flying time per day, and sufficient days off. But under CAP 371 the maximum allowable duty period means that one pilot can’t cover a normal day’s flying, so the operator must hire somebody else to cover just the last 2 or 3 hours, or close up shop while there are still customers wanting to fly. For the small operators which engage in this kind of operation, either option is a severe financial burden.
In the USA, there are separate duty time regulations for unscheduled Part 135 operations, which allow an operator to crew an aircraft for one day with one pilot, but no such option exists in CAP 371. This lack of flexibility may just be the reason why other European countries don’t want to burden their GA operators with its consequences.