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.
I’m afraid the incapacitated crew scenario would be a rather weak justification for keeping auto-trim in ALT law. MS FS players all have joysticks with “Hat switches” that can be used to change trim. I would be surprised if military pilots ever used a trim wheel on their fbw jets.