Dozy:
You're proposing a design change based on a single incident. Don't you think these scenarios have been played out to determine the design parameters? I suspect that the reason trim remains a sidestick function in Alternative Law would be in the case of an incapacitated crew scenario, where the remaining pilot has elevator and trim in their stick hand and throttles in the other, rather than having to dance between the stick, throttles and trim wheel with only two hands. What you're in effect proposing is a straight drop to Direct Law upon loss of air data.
Dozy, are you a pilot?