Incidently both AFM's don't mention anything about climbing at a speed higher than V2 but the current aircraft I fly does, so go figure.
Probably a simple answer upon reflection -
(a) there is no imperative for the OEM to provide overspeed schedule data
(b) your turboprops, I guess, are short range machines (Dash, 340, and similar ?) so the presumption is that a lot of departures are from shorter runways where min speed schedules rule.. ie not much demand for overspeed schedules.
(c) jet ops typically involve longer runways at major aerodromes where the opportunity to squeeze a bit more payload out of a runway is significantly greater
ergo more reason for overspeed scheduling
One very important point with increased V2 considerations which I don't recall seeing noted is - OEI, one should
never attempt to increase V2 from a lower speed to get a better climb due to the distance penalty in the air - while the final climb will be better, the intermediate problem is that the aircraft will probably run under the planned NFP with obvious terrain clearance considerations.
The whole idea of the higher airspeed covers two situations -
(a) if the takeoff is planned with overspeed scheduled speeds, the higher V2 is targetted as part of the OEI takeoff
(b) if the initial takeoff didn't involve a failure, then the airspeed, in all likelihood, will be somewhat above V2 which puts you in a better part of the climb characteristic (gradient curve).
So, in the event of a post-V1 failure, hang on to whatever speed you end up with (after the failure is controlled) within a modest increment band (typically quoted as V2 to V2+20 or so) rather than pitching up to slow down to V2.
If, on the other hand, you are at V2+40, say, then, in the absence of general knowledge regarding your position on the climb characteristic, it is a better practice to pitch up slowly to come back within the AFM-cited overspeed range.