Fernando
Firstly - seperate the discussions about reduced take-off thrust and noise abatement climb! There is no real difference in noise levels. Reduced thrust take-offs are done to extend engine life; noise abate climbs are done to avoid annoying the neighbours. Two different issues.
As to not using derate on a limited runway - a broader discussion is required, because you may be artificially limiting the runway by using reduced thrust!
Let us say that for a given (short) runway at airport AAZZ, a dive into the perf data for a flap15 take off produces an RTOW of 22,100Kgs using a reduced thrust setting.
For a max thrust take off, the RTOW increases to 26,500Kgs. This is the same as the MTOW (Airframe limit) of 26,500Kgs.
The dispatcher now arrives with a loadsheet showing an actual take off weight of 24,200Kgs.
Quite clearly, reduced thrust can not be used and max T/O thrust is the order of the day. If, using Max take off thrust, the V1 at RTOW/MTOW is 134Kts, but the VR at 24,200Kgs is 129Kts, the V1 and VR are both 129 as the decision speed can not be greater than VR (OK?). Another five knots on the V1/Vr, although not good practice, would still allow us to accel/stop on the grey stuff. (And some to spare, because the actual TOW is less than RTOW and the a/c would therefore accel to V1 faster. Also stop faster. (Yes?)
If, however, the loadsheet shows a TOW of 22,050Kgs; this figure is less than the RTOW for a reduced thrust Take off which would then be used in order to extend engine life.
The RTOW is less because the acceleration with reduced thrust is less and it takes longer to accelerate. The V1 is less for the same reason, but in this case, the actual take off weight is quite close to the RTOW. We have in effect artificially made the runway limiting, because our T/O weight is close to the RTOW for the thrust setting.
In this case, you would want to derate the take off to preserve engine life but arbitrarily increasing the V1 figure above that quoted in the perf data would not be a good idea as we are close to RTOW and there would be the risk of overrun in the event of an aborted take off.
On very long runways, where the RTOW would, if calculated, be well above the the MTOW, it would not be a problem stopping in the event of a malfunction. In this case though, I can't see why anyone would want to arbitrarily increase the V1.
As to commenting to your Captain when he adds a few knots to the V1, I would perhaps run it past your performance specialist or Chief Pilot as a hypothetical question first.
Make sure that you fully understand the calculations.
Hope this helps.