Some thoughts ..
(a) "higher speeds ... improved V2 climb technique.. unused distance available on the runway and ... WAT limited "
V2 higher than minimum V2 for the weight will give you a better climb gradient than at minimum V2 .. has nothing to do with whether you are/are not WAT limited. However, with spare runway, and providing that obstacles permit, overspeed can be used to trade that better gradient capability for extra weight to bring you back to WAT-limited. (The mighty dollar rules).
(b) " limiting obstacle, using the higher speeds ... would keep the airplane on the ground longer; TODR increases and the distance to the obstacle reduces".
True .. but it is a case of balancing the thing ... extra distance on the debit, but better climb on the credit. Not a cases of new obstacles popping up .. the analysis looks at all obstacles and figures the RTOW on the critical set of obstacles for the weight and speed schedule combination.
(c) there are other pros and cons with speed choices .. eg, lower V2 make the flying more critical and the obstacle clearance further out worse ... higher speeds add to aircraft wear and tear and eat into the ASD pads.
(d) speeds have to be consistent with an analysis. .. so, for instance, you can't pick this V1 and mix it with that VR and V2. Otherwise, you pick one according to you preferences.