I would say definitely not necessary. I think it makes little difference for a carry/defensive pistol. Maybe you could argue for a competition pistol where you are chasing the fastest splits possible, it might be a benefit depending on skill, etc. I had a very similar experience where I was running CGW pro-packages with the CGW trigger and it’s over travel screw in my 3 SP01’s (that I use for carry and comp) but switched them out to CZ custom flat DA/SA triggers (which lack overtravel screws) and noticed no significant difference. My splits actually improved very slightly on average. But, I think that is more related to the CZC trigger profile being more optimal for how I grip the gun and my hand shape/finger length.
I think a strong argument could be made that for a defensive gun an overtravel screw is just another potential failure point (albeit very unlikely if it is adjusted and appropriate threadlocker is used). So something to consider there as well.
Another factor is that I found for my Al-alloy frame P01 omegas the steel overtravel screw from the CGW triggers would actually wear an ident into the frame after significant dry fire / live fire. This renders the screw useless or at least in need of continual adjustment for it to have any effect.