As I understand it the underlying reason isn't to inhibit the stall warning below 60 it's to prevent spurious data when the airflow is outside the vanes spec. Stalled or not stalled, a warning that airspeed is less than 60 knots when there is no weight on the wheels would be equivalent. If that situation can only arise when stalled, then fair enough allow a warning. Seems quixotic to cancel an existing warning when the speed goes out of range and it is likely that that very same stall caused the speed to go out of range.
Hope it's allowed to quote myself when I subsequently disagree. After a bit more thought I would give the designers some slack on this. Reasonable (and correct in this instance) to think that the stall warner would have done its job as best it could, well before speed decayed to 60knots. Can't blame the messenger if no-one gives it credence. My supposition is that it was discounted when it was real the first time round but believed when it reactivated on ND.