Under the old system there were 15 squads starting at the same time on 15 different stands if there are less stands and different amount of targets on each stand you then get bottle necks as the three pairs finished early and the 5 pair finished late. So as James said 120 goes equally into 15 stands and makes it run smoothly.
It's not a problem on normal registered unsquaded shoots where you can jump a stand or squadded ones that start from the first stand that work round in order and you only have a total of about 100 shooters to get through.
Also sportrap and skeet etc are immune as they are shot on a fixed layout and the next squad is booked on at a time which coincides when they finish with less entrants.
Putting extra stands on incurs extra costs, refs traps etc.so it is going to cost the ground owner extra to put on the 120 bird shoot other than just clays.
If you want to shoot a shoot that resembles live shooting then shoot flushes or we could design a discipline that resembles rough shooting which means your score could be 5 ex 9 for the first shooter and 0 ex 0 for the second.
I really don't get the issue with the extra 20 birds.