As usual this is not as simple as it seems. EGR (exhaust gas recirculation) uses a small amount of exhaust, which is basically inert and will not support additional combustion, to lower cylinder temperatures and pressures to reduce NOx production. It only functions at low output levels (idle, light throttle) and is not functioning during full throttle and therefore will not decrease full throttle power output or response.
Because of this effect the engineers program the computer with a more aggressive and less fuel. Now, if the EGR fails this timing and fuel curve will cause detonation... so... on OBDI and OBDII vehicles, if the EGR function fails the computer automatically reduces timing and adds fuel. This will NOT help performance. As pointed out above the EGR does not function during full throttle operation.
The most usual effect of deleting the EGR is light throttle pinging.
While seemingly reducing complication... deleting EGR will not enhance performance and probably cause negative operation. Full throttle performance may or may not be affected.
BTW, on the VVTi engines the valve overlap is increased by the computer to create the EGR effect and that is why there is no external EGR plumbing on these engines.