Three comments:
1. Many airlines do not credit credit miles on their own FFP for the cheapest fares of partners.
CX P fares have been around for a few years and BAEC is, of course, well aware of it and decided not to credit any avios rather than the 125% for a bit more expensive biz fares. SAme for O, zero avios rather than 25% for slightly more expensive fares.

2. T&Cs of all airlines prohibit dales a miles/redemption tickets. Trip.com is a major OTA, it will never risk a retaliation from a major airlines by selling redemption tickets from someone else. Maybe that happened decades ago.

3. Using a major OTA (like trip.com) can work fine as long as you don't need to change the ticket/flight. But in case of flight cancellation or voluntary flight change, it can be a major hassle.