In calculating the accelerate-stop distances, what are the possible reasons why the use of reverse thrust is not taken into account on a dry runway, while it is taken into account on a wet runway? What's the rationale behind this diffentiation, when at least as I see it there's nothing that prevents the use of reverse thrust on a dry runway for an aborted takeoff?
If your thrust reversers are operational and debris is not a concern, you're right for an in-service rejected takeoff (RTO):
There's nothing that prevents the use of reverse thrust on a dry runway for an aborted takeoff.
Most in-service RTOs utilize reverse thrust if available (see this video for a dry-runway example).
However, in order to certify a transport-category airplane, one must show compliance with 14 CFR 25.109, paragraph (f), which precludes the use of thrust reversers on dry runways in calculating the accelerate-stop distance. The demonstration required by paragraph (i), therefore, cannot be conducted with reverse thrust on a dry runway. From a certification standpoint, the accelerate-stop calculation is made the way it is because that's what the regulations say. But why is the law written this way? See this video at about 1:12:
The whole intent is to demonstrate [that] under [the] worst conditions you can safely stop the aircraft.
"Worst conditions" encompasses at least inoperative thrust reversers and worn brakes.