It's much easier to manage GS with 12 players (but 2 or 3 of them are scrubs, who will play in the scrimmage).
If you think about it, say you have 8 players roster. The average minutes each player will receive every week would be; 90 minutes (48*5*3/8), which is too much. If you have 12 players roster, the average minutes each player will receive every week would be; 60 minutes, which is very very ideal.
I'm not saying everybody will play exactly 60 minutes...because that's almost impossible, but on average, playing 60 minutes and 90 minutes is a huge difference. 90 minutes will drop the GS, increase the chance of injury etc compared to 60 minutes. Ofc when you have 8 players roster as an example, you could always play 3 players for the scrimmage etc, but anyway, having 12 players will be much easier to manage GS (unless u're training GS every week).